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Algebra and Trigonometry

Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Chapter 10

Analytic Geometry Topics - all with Video Answers

Educators

AG

Section 1

The Parabola

01:05

Problem 1

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Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$x^{2}=8 y$$

AG
Ankit Gupta
Numerade Educator
00:59

Problem 2

Text Unavailable

Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$y^{2}=-10 x$$

AG
Ankit Gupta
Numerade Educator
01:09

Problem 3

Text Unavailable

Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$(y-2)^{2}=-3(x+4)$$

AG
Ankit Gupta
Numerade Educator
01:38

Problem 4

Text Unavailable

Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$(x+1)^{2}=5(y-2)$$

AG
Ankit Gupta
Numerade Educator
01:39

Problem 5

Text Unavailable

Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$13 x^{2}-8 y-9=0$$

AG
Ankit Gupta
Numerade Educator
01:51

Problem 6

Text Unavailable

Match the equation with one of the graphs $(a)-(f),$ which follow.
A.(Graph cannot copy)
B.(Graph cannot copy)
C.(Graph cannot copy)
D.(Graph cannot copy)
E.(Graph cannot copy)
F.(Graph cannot copy)
$$41 x+6 y^{2}=12$$

AG
Ankit Gupta
Numerade Educator
01:18

Problem 7

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}=20 y$$

AG
Ankit Gupta
Numerade Educator
01:14

Problem 8

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}=16 y$$

AG
Ankit Gupta
Numerade Educator
01:30

Problem 9

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}=-6 x$$

AG
Ankit Gupta
Numerade Educator
01:30

Problem 10

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Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}=-2 x$$

AG
Ankit Gupta
Numerade Educator
03:39

Problem 11

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}-4 y=0$$

AG
Ankit Gupta
Numerade Educator
03:27

Problem 12

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}+4 x=0$$

AG
Ankit Gupta
Numerade Educator
03:08

Problem 13

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$x=2 y^{2}$$

AG
Ankit Gupta
Numerade Educator
02:42

Problem 14

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Find the vertex, the focus, and the directrix. Then draw the graph.
$$y=\frac{1}{2} x^{2}$$

AG
Ankit Gupta
Numerade Educator
01:50

Problem 15

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Find an equation of a parabola satisfying the given conditions.
Focus $(4,0),$ directrix $x=-4$

AG
Ankit Gupta
Numerade Educator
01:34

Problem 16

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Find an equation of a parabola satisfying the given conditions.
$$\text { Focus }\left(0, \frac{1}{4}\right), \text { directrix } y=-\frac{1}{4}$$

AG
Ankit Gupta
Numerade Educator
01:32

Problem 17

Text Unavailable

Find an equation of a parabola satisfying the given conditions.
Focus $(0,-\pi),$ directrix $y=\pi$

AG
Ankit Gupta
Numerade Educator
01:44

Problem 18

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Find an equation of a parabola satisfying the given conditions.
$$\text { Focus }(-\sqrt{2}, 0), \operatorname{directrix} x=\sqrt{2}$$

AG
Ankit Gupta
Numerade Educator
02:10

Problem 19

Text Unavailable

Find an equation of a parabola satisfying the given conditions.
Focus $(3,2),$ directrix $x=-4$

AG
Ankit Gupta
Numerade Educator
01:27

Problem 20

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Find an equation of a parabola satisfying the given conditions.
Focus $(-2,3),$ directrix $y=-3$

AG
Ankit Gupta
Numerade Educator
04:25

Problem 21

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Find the vertex, the focus, and the directrix. Then draw the graph.
(x+2)^{2}=-6(y-1)

AG
Ankit Gupta
Numerade Educator
04:51

Problem 22

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Find the vertex, the focus, and the directrix. Then draw the graph.
$$(y-3)^{2}=-20(x+2)$$

AG
Ankit Gupta
Numerade Educator
05:59

Problem 23

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Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}+2 x+2 y+7=0$$

AG
Ankit Gupta
Numerade Educator
05:52

Problem 24

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}+6 y-x+16=0$$

AG
Ankit Gupta
Numerade Educator
05:06

Problem 25

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Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}-y-2=0$$

AG
Ankit Gupta
Numerade Educator
04:47

Problem 26

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$x^{2}-4 x-2 y=0$$

AG
Ankit Gupta
Numerade Educator
04:36

Problem 27

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y=x^{2}+4 x+3$$

AG
Ankit Gupta
Numerade Educator
04:48

Problem 28

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y=x^{2}+6 x+10$$

AG
Ankit Gupta
Numerade Educator
04:48

Problem 28

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}-y-x+6=0$$

AG
Ankit Gupta
Numerade Educator
04:21

Problem 29

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}-y-x+6=0$$

AG
Ankit Gupta
Numerade Educator
05:04

Problem 30

Text Unavailable

Find the vertex, the focus, and the directrix. Then draw the graph.
$$y^{2}+y-x-4=0$$

AG
Ankit Gupta
Numerade Educator
02:38

Problem 31

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An engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening, and the focus is placed 4 ft from the vertex.
(image cannot copy)
a) Position a coordinate system with the origin at the vertex and the $x$ -axis on the parabola's axis of symmetry and find an equation of the parabola.
b) Find the depth of the satellite dish at the vertex.

AG
Ankit Gupta
Numerade Educator
02:15

Problem 32

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Flashlight Mirror. A heavy-duty flashlight mirror has a parabolic cross section with diameter 6 in. and depth 1 in.
(Image cannot copy)
a) Position a coordinate system with the origin at the vertex and the $x$ -axis on the parabola's axis of symmetry and find an equation of the parabola.
b) How far from the vertex should the bulb be positioned if it is to be placed at the focus?

AG
Ankit Gupta
Numerade Educator
01:36

Problem 33

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A spotlight has a parabolic cross section that is $4 \mathrm{ft}$ wide at the opening and $1.5 \mathrm{ft}$ deep at the vertex. How far from the vertex is the focus?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:53

Problem 34

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A field microphone used at a football game has a parabolic cross section and is 18 in. deep. The focus is 4 in. from the vertex. Find the width of the microphone at the opening.

AG
Ankit Gupta
Numerade Educator
01:28

Problem 35

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which has/have $x$ -intercept $\left(\frac{2}{3}, 0\right) ?$

AG
Ankit Gupta
Numerade Educator
01:16

Problem 36

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which has/have $y$ -intercept $(0,7) ?$

AG
Ankit Gupta
Numerade Educator
01:47

Problem 37

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which slant up from left to right?

AG
Ankit Gupta
Numerade Educator
00:59

Problem 38

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which has the least steep slant?

AG
Ankit Gupta
Numerade Educator
00:25

Problem 39

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which has/have slope $\frac{1}{3} ?$

AG
Ankit Gupta
Numerade Educator
00:59

Problem 40

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which, if any, contain the point $(3,7) ?$

AG
Ankit Gupta
Numerade Educator
01:09

Problem 41

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which, if any, are parallel?

AG
Ankit Gupta
Numerade Educator
02:22

Problem 42

Text Unavailable

Consider the following linear equations. Without graphing them, answer the questions below.
a) $y=2 x$
b) $y=\frac{1}{3} x+5$
c) $y=-3 x-2$
d) $y=-0.9 x+7$
e) $y=-5 x+3$
f) $y=x+4$
g) $8 x-4 y=7$
h) $3 x+6 y=2$
Which, if any, are perpendicular?

AG
Ankit Gupta
Numerade Educator
01:51

Problem 43

Text Unavailable

Find an equation of the parabola with a vertical axis of symmetry and vertex $(-1,2)$ and containing the point $(-3,1)$

AG
Ankit Gupta
Numerade Educator
02:12

Problem 44

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Find an equation of a parabola with a horizontal axis of symmetry and vertex $(-2,1)$ and containing the point $(-3,5)$

AG
Ankit Gupta
Numerade Educator
05:12

Problem 45

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Suspension Bridge. The parabolic cables of a $200-\mathrm{ft}$ portion of the roadbed of a suspension bridge are positioned as shown at right. Vertical cables are to be spaced every $20 \mathrm{ft}$ along this portion of the roadbed. Calculate the lengths of these vertical cables.

AG
Ankit Gupta
Numerade Educator