• Home
  • Textbooks
  • Intermediate Algebra for College Students
  • Conic Sections

Intermediate Algebra for College Students

Allen R. Angel; Dennis C. Runde

Chapter 10

Conic Sections - all with Video Answers

Educators

Section 1

The Parabola and the Circle

01:16

Problem 1

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The formula, midpoint $=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$, is called the the ____________ formula.

AG
Ankit Gupta
Numerade Educator
00:23

Problem 2

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The formula, $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$, is called the __________ formula.

AG
Ankit Gupta
Numerade Educator
00:23

Problem 3

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The equation $y=a(x-h)^{2}+k$ is the equation of a ___________.

AG
Ankit Gupta
Numerade Educator
01:19

Problem 4

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The equation $x^{2}+y^{2}=r^{2}$ is the equation of a circle with center at _______ and radius $r$.

K Joseph
K Joseph
Numerade Educator
01:19

Problem 5

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The equation $(x-h)^{2}+(y-k)^{2}=r^{2}$ is the equation of a circle with center at _______ and radius $r$.

K Joseph
K Joseph
Numerade Educator
00:24

Problem 6

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$\text { distance } \quad \text { (0,0) } \quad \text { parabola } \quad \text { circle } \quad \text { (k, h)}\quad \text { (h, k) } \quad \text { (x, y)} \quad \text { midpoint}$
The four conic sections are the parabola, ellipse, _________ and hyperbola.

AG
Ankit Gupta
Numerade Educator
01:31

Problem 7

Graph each equation.
$$
y=(x-2)^{2}-1
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:44

Problem 8

Graph each equation.
$$
y=(x+3)^{2}-4
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
View

Problem 9

Graph each equation.
$$
y=(x+3)^{2}+2
$$

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 10

Graph each equation.
$$
y=(x-2)^{2}+3
$$

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 11

Graph each equation.
$$
y=-(x-1)^{2}+1
$$

Victor Salazar
Victor Salazar
Numerade Educator
01:58

Problem 12

Graph each equation.
$$
y=-(x+3)^{2}+4
$$

Mary Brese
Mary Brese
Numerade Educator
01:31

Problem 13

Graph each equation.
$$
y=-(x-2)^{2}-1
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
View

Problem 14

Graph each equation.
$$
y=-(x+4)^{2}-5
$$

Victor Salazar
Victor Salazar
Numerade Educator
01:27

Problem 15

Graph each equation.
$$
y=2(x-2)^{2}-8
$$

Alison Rodriguez
Alison Rodriguez
Numerade Educator
View

Problem 16

Graph each equation.
$$
y=2(x+1)^{2}-3
$$

Victor Salazar
Victor Salazar
Numerade Educator
00:55

Problem 17

Graph each equation.
$$
y=-3(x-5)^{2}+3
$$

Amrita Bhasin
Amrita Bhasin
Numerade Educator
01:27

Problem 18

Graph each equation.
$$
y=-2(x+1)^{2}+8
$$

Alison Rodriguez
Alison Rodriguez
Numerade Educator
View

Problem 19

Graph each equation.
$$
x=-(y-5)^{2}+4
$$

Victor Salazar
Victor Salazar
Numerade Educator
View

Problem 20

Graph each equation.
$$
x=-(y-2)^{2}+1
$$

Victor Salazar
Victor Salazar
Numerade Educator
01:44

Problem 21

Graph each equation.
$$
x=(y-4)^{2}-3
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
View

Problem 22

Graph each equation.
$$
x=(y-1)^{2}+1
$$

Victor Salazar
Victor Salazar
Numerade Educator
00:55

Problem 23

Graph each equation.
$$
x=3(y+1)^{2}+5
$$

Amrita Bhasin
Amrita Bhasin
Numerade Educator
07:05

Problem 24

Graph each equation.
$$
x=-2(y+4)^{2}-3
$$

Natalie Anderson
Natalie Anderson
Numerade Educator
01:21

Problem 25

Graph each equation.
$$
y=-2\left(x+\frac{1}{2}\right)^{2}+6
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
View

Problem 26

Graph each equation.
$$
y=-\left(x-\frac{5}{2}\right)^{2}+\frac{1}{2}
$$

Victor Salazar
Victor Salazar
Numerade Educator
01:43

Problem 27

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=x^{2}+2 x
$$

Gregory Higby
Gregory Higby
Numerade Educator
01:11

Problem 28

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=x^{2}-4 x
$$

Babita Kumari
Babita Kumari
Numerade Educator
01:04

Problem 29

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=y^{2}-6 y
$$

Babita Kumari
Babita Kumari
Numerade Educator
01:43

Problem 30

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=y^{2}+4 y
$$

Gregory Higby
Gregory Higby
Numerade Educator
03:19

Problem 31

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=x^{2}+4 x+5
$$

Suzanne W.
Suzanne W.
Numerade Educator
03:19

Problem 32

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=x^{2}+2 x-7
$$

Suzanne W.
Suzanne W.
Numerade Educator
04:19

Problem 33

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=y^{2}+6 y+8
$$

Kelsey Dondelinger
Kelsey Dondelinger
Numerade Educator
01:43

Problem 34

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=y^{2}+4 y+3
$$

Gregory Higby
Gregory Higby
Numerade Educator
01:03

Problem 35

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=-y^{2}+6 y-9
$$

Xiaomeng Zhang
Xiaomeng Zhang
Numerade Educator
01:11

Problem 36

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=-x^{2}+4 x-4
$$

Babita Kumari
Babita Kumari
Numerade Educator
03:19

Problem 37

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=-y^{2}-2 y+5
$$

Suzanne W.
Suzanne W.
Numerade Educator
03:19

Problem 38

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=-y^{2}+6 y-5
$$

Suzanne W.
Suzanne W.
Numerade Educator
03:19

Problem 39

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=x^{2}+7 x+10
$$

Suzanne W.
Suzanne W.
Numerade Educator
01:11

Problem 40

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=-y^{2}+3 y-4
$$

Babita Kumari
Babita Kumari
Numerade Educator
01:04

Problem 41

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
x=3 y^{2}-12 y-36
$$

Babita Kumari
Babita Kumari
Numerade Educator
01:11

Problem 42

In Exercises 27-42, a) Write the equation in the form $y=a(x-h)^{2}+k$ or $x=a(y-k)^{2}+h$. b) Graph the equation.
$$
y=2 x^{2}-4 x-4
$$

Babita Kumari
Babita Kumari
Numerade Educator
00:37

Problem 43

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(4,7) \text { and }(7,11)
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:52

Problem 44

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(1,3) \text { and }(6,15)
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
00:42

Problem 45

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(-1,-3) \text { and }(4,9)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:41

Problem 46

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(-4,-7) \text { and }(2,1)
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:08

Problem 47

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(-4,-5) \text { and }(5,-2)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:18

Problem 48

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(6,7) \text { and }(11,0)
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
00:52

Problem 49

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(3,-1) \text { and }\left(\frac{1}{2}, 4\right)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:55

Problem 50

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
\left(-\frac{1}{4}, 2\right) \text { and }\left(-\frac{3}{2}, 6\right)
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
00:47

Problem 51

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(-1.6,3.5) \text { and }(-4.3,-1.7)
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:46

Problem 52

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.

Jennifer White
Jennifer White
Numerade Educator
00:49

Problem 53

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(\sqrt{7}, \sqrt{3}) \text { and }(0,0)
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
01:08

Problem 54

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(-\sqrt{2},-\sqrt{5}) \text { and }(0,0)
$$

Nez Nikoo
Nez Nikoo
Numerade Educator
00:33

Problem 55

Determine the midpoint of the line segment between each pair of points.
$$
(1,3) \text { and }(5,7)
$$

James Kiss
James Kiss
Numerade Educator
00:59

Problem 56

Determine the midpoint of the line segment between each pair of points.
$$
(4,7) \text { and }(6,11)
$$

Charles Carter
Charles Carter
Numerade Educator
00:55

Problem 57

Determine the midpoint of the line segment between each pair of points.
$$
(-8,3) \text { and }(4,-15)
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:35

Problem 58

Determine the midpoint of the line segment between each pair of points.
$$
(-8,-9) \text { and }(-6,-3)
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 59

Determine the midpoint of the line segment between each pair of points.
$$
(-1,4) \text { and }(4,6)
$$

Charles Carter
Charles Carter
Numerade Educator
01:07

Problem 60

Determine the midpoint of the line segment between each pair of points.
$$
(4,9) \text { and }(1,-5)
$$

Julie Silva
Julie Silva
Numerade Educator
01:01

Problem 61

Determine the midpoint of the line segment between each pair of points.
$$
\left(3, \frac{1}{2}\right) \text { and }(2,-4)
$$

Charles Carter
Charles Carter
Numerade Educator
01:57

Problem 62

Determine the midpoint of the line segment between each pair of points.
$$
\left(\frac{5}{2^{\prime}}, 1\right) \text { and }\left(2, \frac{9}{2}\right)
$$

AG
Ankit Gupta
Numerade Educator
01:48

Problem 63

Determine the midpoint of the line segment between each pair of points.
$$
(\sqrt{3}, 2) \text { and }(\sqrt{2}, 5)
$$

Marcella Sippey
Marcella Sippey
Numerade Educator
01:07

Problem 64

Determine the midpoint of the line segment between each pair of points.
$$
(-\sqrt{7}, 8) \text { and }(\sqrt{5}, \sqrt{3})
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:20

Problem 65

Write the equation of each circle with the given center and radius.
Center $(0,0)$, radius 5

Charles Carter
Charles Carter
Numerade Educator
00:41

Problem 66

Write the equation of each circle with the given center and radius.
Center $(0,0)$, radius 9

Heather Zimmers
Heather Zimmers
Numerade Educator
01:42

Problem 67

Write the equation of each circle with the given center and radius.
Center $(2,0)$, radius 8

Mary Brese
Mary Brese
Numerade Educator
01:08

Problem 68

Write the equation of each circle with the given center and radius.
Center $(-3,0)$, radius 7

Mary Brese
Mary Brese
Numerade Educator
00:36

Problem 69

Write the equation of each circle with the given center and radius.
Center $(0,-6)$, radius 10

Alison Rodriguez
Alison Rodriguez
Numerade Educator
00:16

Problem 70

Write the equation of each circle with the given center and radius.
Center $(0,5)$, radius 2

Charles Carter
Charles Carter
Numerade Educator
00:40

Problem 71

Write the equation of each circle with the given center and radius.
Center $(7,-6)$, radius 12

Heather Zimmers
Heather Zimmers
Numerade Educator
01:08

Problem 72

Write the equation of each circle with the given center and radius.
Center $(-5,2)$, radius 3

Mary Brese
Mary Brese
Numerade Educator
01:51

Problem 73

Write the equation of each circle with the given center and radius.
Center $(-6,-5)$, radius 11

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:40

Problem 74

Write the equation of each circle with the given center and radius.
Center $(-6,-1)$, radius 15

Heather Zimmers
Heather Zimmers
Numerade Educator
00:40

Problem 75

Write the equation of each circle with the given center and radius.
Center $(-7,-2)$, radius $\sqrt{13}$

Christopher Stanley
Christopher Stanley
Numerade Educator
01:08

Problem 76

Write the equation of each circle with the given center and radius.
Center $(1,2)$, radius $\sqrt{5}$

Mary Brese
Mary Brese
Numerade Educator
02:14

Problem 77

Determine the equation of each circle. Assume the radius is a whole number.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
02:14

Problem 78

Determine the equation of each circle. Assume the radius is a whole number.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
02:14

Problem 79

Determine the equation of each circle. Assume the radius is a whole number.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
02:14

Problem 80

Determine the equation of each circle. Assume the radius is a whole number.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
01:56

Problem 81

Graph each equation.
$$
x^{2}+y^{2}=16
$$

Mary Brese
Mary Brese
Numerade Educator
02:11

Problem 82

Graph each equation.
$$
x^{2}+y^{2}=9
$$

Mary Brese
Mary Brese
Numerade Educator
02:11

Problem 83

Graph each equation.
$$
x^{2}+y^{2}=10
$$

Mary Brese
Mary Brese
Numerade Educator
View

Problem 84

Graph each equation.
$$
x^{2}+y^{2}=5
$$

Victor Salazar
Victor Salazar
Numerade Educator
03:06

Problem 85

Graph each equation.
$$
(x+4)^{2}+y^{2}=25
$$

James Schroeder
James Schroeder
Numerade Educator
02:12

Problem 86

Graph each equation.
$$
x^{2}+(y+1)^{2}=9
$$

Mary Brese
Mary Brese
Numerade Educator
03:43

Problem 87

Graph each equation.
$$
(x+1)^{2}+(y-4)^{2}=9
$$

James Schroeder
James Schroeder
Numerade Educator
01:08

Problem 88

Graph each equation.
$$
(x-2)^{2}+(y+3)^{2}=16
$$

Christopher Stanley
Christopher Stanley
Numerade Educator
01:27

Problem 89

Graph each equation.
$$
(x+8)^{2}+(y+2)^{2}=9
$$

Alison Rodriguez
Alison Rodriguez
Numerade Educator
01:43

Problem 90

Graph each equation.
$$
(x+3)^{2}+(y-4)^{2}=36
$$

Mary Brese
Mary Brese
Numerade Educator
02:40

Problem 91

Graph each equation.
$$
y=\sqrt{25-x^{2}}
$$

Alison Rodriguez
Alison Rodriguez
Numerade Educator
00:52

Problem 92

Graph each equation.
$$
y=\sqrt{16-x^{2}}
$$

James Kiss
James Kiss
Numerade Educator
01:50

Problem 93

Graph each equation.
$$
y=-\sqrt{4-x^{2}}
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:51

Problem 94

Graph each equation.
$$
y=-\sqrt{49-x^{2}}
$$

Christopher Stanley
Christopher Stanley
Numerade Educator
02:15

Problem 95

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+8 x+15=0
$$

Julie Silva
Julie Silva
Numerade Educator
01:52

Problem 96

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+4 y=0
$$

Sujit Kumar
Sujit Kumar
Numerade Educator
00:55

Problem 97

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+6 x-4 y+4=0
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:52

Problem 98

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+2 x-4 y-4=0
$$

Sujit Kumar
Sujit Kumar
Numerade Educator
00:50

Problem 99

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+6 x-2 y+6=0
$$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:50

Problem 100

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+4 x-6 y-3=0
$$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:14

Problem 101

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}+3 x-y-\frac{13}{2}=0
$$

Vicki Stebbins
Vicki Stebbins
Numerade Educator
03:11

Problem 102

In Exercises 95-102, a) use the method of completing the square to write each equation in standard form. b) Graph the equation.
$$
x^{2}+y^{2}-x+3 y-\frac{3}{2}=0
$$

Kader Bayar
Kader Bayar
Numerade Educator
01:01

Problem 103

Determine the area of the circle in Exercise 85 .

Nick Johnson
Nick Johnson
Numerade Educator
01:01

Problem 104

Determine the area of the circle in Exercise $87 .$

Nick Johnson
Nick Johnson
Numerade Educator
00:37

Problem 105

In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation.
$$
x=y^{2}-6 y-7
$$

Xiaomeng Zhang
Xiaomeng Zhang
Numerade Educator
02:22

Problem 106

In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation.
$$
x=-y^{2}+8 y-12
$$

Luke Waitrovich
Luke Waitrovich
Numerade Educator
02:45

Problem 107

In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation.
$$
x=2(y-3)^{2}+6
$$

Raushan Kumar
Raushan Kumar
Numerade Educator
00:36

Problem 108

In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation.
$$
x=-(y+2)^{2}-8
$$

Xiaomeng Zhang
Xiaomeng Zhang
Numerade Educator
00:31

Problem 109

Determine the length of the line segment whose midpoint is $(4,-6)$ with one endpoint at $(7,-2)$.

Zach Steedman
Zach Steedman
Numerade Educator
00:55

Problem 110

Determine the length of the line segment whose midpoint is $(-2,4)$ with one endpoint at $(3,6)$.

James Kiss
James Kiss
Numerade Educator
00:44

Problem 111

Determine the equation of a circle with center at $(-6,2)$ that is tangent to the $x$-axis (that is, the circle touches the $x$-axis at only one point).

James Kiss
James Kiss
Numerade Educator
00:39

Problem 112

Determine the equation of a circle with center at $(-3,5)$ that is tangent to the $y$-axis.

Charles Carter
Charles Carter
Numerade Educator
02:42

Problem 113

In Exercises 113 and 114 , determine a) the radius of the circle whose diameter is along the line shown, b) the center of the circle, and c) the equation of the circle.

Erika Bustos
Erika Bustos
Numerade Educator
02:42

Problem 114

In Exercises 113 and 114 , determine a) the radius of the circle whose diameter is along the line shown, b) the center of the circle, and c) the equation of the circle.

Erika Bustos
Erika Bustos
Numerade Educator
00:25

Problem 115

What is the maximum number and the minimum number of points of intersection possible for the graphs of $y=a\left(x-h_{1}\right)^{2}+k_{1}$ and $x=a\left(y-k_{2}\right)^{2}+h_{2}$ ? Explain.

Trinity Steen
Trinity Steen
Numerade Educator
04:31

Problem 116

Consider the equations $x^{2}+y^{2}=16$ and $(x-2)^{2}+(y-2)^{2}=16$. By considering the center and radius of each circle, determine the number of points of intersection of the two circles.

Nick Johnson
Nick Johnson
Numerade Educator
01:50

Problem 117

The Ferris wheel at Navy Pier in Chicago is 150 feet tall. The radius of the wheel itself is $68.2$ feet.

AG
Ankit Gupta
Numerade Educator
07:29

Problem 118

A highway department is planning to construct a semicircular one-way tunnel through a mountain. The tunnel is to be large enough so that a truck 8 feet wide and 10 feet tall will pass through the center of the tunnel with 1 foot to spare directly above the corner of the truck when it is driving down the center of the tunnel (as shown in the figure below). Determine the minimum radius of the tunnel.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
03:20

Problem 119

Consider the figure on top of the next page. Write an equation for
a) the blue circle,
b) the red circle, and
c) the green circle.
d) Determine the shaded area.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:41

Problem 120

Consider the figure below.
a) Determine the area of the triangle outlined in green.
b) When a triangle is inscribed within a parabola, as in the figure, the area within the parabola from the base of the triangle is $\frac{4}{3}$ the area of the triangle. Determine the area within the parabola from $x=-3$ to $x=3$.

Chelsea Green
Chelsea Green
Numerade Educator
01:03

Problem 121

Determine the area between the two concentric circles whose equations are $(x-2)^{2}+(y+4)^{2}=16$ and $(x-2)^{2}+$ $(y+4)^{2}=64$. Concentric circles are circles that have the same center.

Nick Johnson
Nick Johnson
Numerade Educator
02:33

Problem 122

Determine the shaded area of the square in the figure. The equation of the circle is $x^{2}+y^{2}=9$.

Lucas Finney
Lucas Finney
Numerade Educator
01:24

Problem 123

If you know one endpoint of a line segment and the length of the line segment, can you determine the other endpoint? Explain.

Linh Vu
Linh Vu
Numerade Educator
01:02

Problem 124

If you know the midpoint of a line segment, is it possible to determine the length of the line segment? Explain.

Erika Bustos
Erika Bustos
Numerade Educator
01:09

Problem 125

Will all parabolas of the form $y=a(x-h)^{2}+k, a>0$ be functions? Explain. What will be the domain and range of $y=a(x-h)^{2}+k, a>0$ ?

AG
Ankit Gupta
Numerade Educator
00:40

Problem 126

Will all parabolas of the form $x=a(y-k)^{2}+h, a>0$ be functions? Explain. What will be the domain and range of $x=a(y-k)^{2}+h, a>0$ ?

Sriram Soundarrajan
Sriram Soundarrajan
Numerade Educator
01:43

Problem 127

How will the graphs of $y=2(x-3)^{2}+4$ and $y=-2(x-3)^{2}+4$ compare?

Charles Carter
Charles Carter
Numerade Educator
00:20

Problem 128

What is the definition of a circle?

James Kiss
James Kiss
Numerade Educator
00:44

Problem 129

Is $x^{2}-y^{2}=9$ an equation for a circle? Explain.

Linh Vu
Linh Vu
Numerade Educator
00:44

Problem 130

Is $-x^{2}+y^{2}=25$ an equation for a circle? Explain.

Linh Vu
Linh Vu
Numerade Educator
00:44

Problem 131

Is $2 x^{2}+3 y^{2}=6$ an equation for a circle? Explain.

Linh Vu
Linh Vu
Numerade Educator
00:35

Problem 132

Is $x=y^{2}-6 y+3$ an equation for a parabola? Explain.

Adam Dehollander
Adam Dehollander
Numerade Educator
00:35

Problem 133

Is $x^{2}=y^{2}-6 y+3$ an equation for a parabola? Explain.

Adam Dehollander
Adam Dehollander
Numerade Educator
00:59

Problem 134

Is $x=y+2$ an equation for a parabola? Explain.

Heather Zimmers
Heather Zimmers
Numerade Educator
06:34

Problem 135

Discuss and answer Exercise 135 as a group.
The equation of a parabola can be determined if three points on the parabola are known. To do so, start with $y=a x^{2}+b x+c$. Then substitute the $x$ - and $y$-coordinates of the first point into the equation. This will result in an equation in $a, b$, and $c$. Repeat the procedure for the other two points. This process yields a system of three equations in three variables. Next, solve the system for $a, b$, and $c$. To determine the equation of the parabola, substitute the values determined for $a, b$, and $c$ into the equation $y=a x^{2}+b x+c$.
Three points on a parabola are $(0,12),(3,-3)$, and $(-2,32)$.
a) Individually, determine a system of equations in three variables that can be used to determine the equation of the parabola. Then compare your answers. If each member of the group does not have the same system, determine why.
b) Individually, solve the system and determine the values of $a, b$, and $c$. Then compare your answers.
c) Individually, write the equation of the parabola passing through $(0,12),(3,-3)$, and $(-2,32)$. Then compare your answers.
d) Individually, write the equation in
$$
y=a(x-h)^{2}+k
$$
form. Then compare your answers.
e) Individually, graph the equation in part d). Then compare your answers.

Bobby Barnes
Bobby Barnes
University of North Texas
02:17

Problem 136

Simplify $\frac{6 x^{-3} y^{4}}{18 x^{-2} y^{3}}$

AG
Ankit Gupta
Numerade Educator
01:15

Problem 137

Solve the inequality $-4<3 x-4<17$. Write the solution in interval notation.

Melissa Barry
Melissa Barry
Numerade Educator
01:54

Problem 138

Evaluate the determinant.
$$
\left|\begin{array}{rrr}
4 & 0 & 3 \\
5 & 2 & -1 \\
3 & 6 & 4
\end{array}\right|
$$

Caleb Wood
Caleb Wood
Numerade Educator
01:41

Problem 139

a) Write expressions to represent each of the four areas shown in the figure.
b) Express the total area shown as the square of a binomial.

Suzanne W.
Suzanne W.
Numerade Educator
01:13

Problem 140

Graph $y=(x-4)^{2}+1$

James Kiss
James Kiss
Numerade Educator