Section 1
Distance and Midpoint Formulas; Circles
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.$(2,0)$ and $(5,4)$
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.( $-4,-3$ ) and ( 2,5 )
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.(-4, -3) and (8, 2)
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.(-7, -3) and (8, 5)
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.(-1, 4) and (2, 0)
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.( $-1,3$ ) and ( $5,-5$ )
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.( $1,-4$ ) and ( 6,8 )
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.(-8, -2) and (7, 6)
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.$(-3,-5)$ and $(0,1)$
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.$(-1,-2)$ and $(-3,4)$
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.$(3,-1)$ and $(1,7)$
In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.$(-4,-5)$ and $(7,4)$
In the following exercises, (a) find the midpoint of the line segments whose endpoints are given and (b) plot the endpoints and the midpoint on a rectangular coordinate system.$(0,-5)$ and $(4,-3)$
In the following exercises, (a) find the midpoint of the line segments whose endpoints are given and (b) plot the endpoints and the midpoint on a rectangular coordinate system.(-2, -6) and (6, -2)
In the following exercises, (a) find the midpoint of the line segments whose endpoints are given and (b) plot the endpoints and the midpoint on a rectangular coordinate system.$(3,-1)$ and $(4,-2)$
In the following exercises, (a) find the midpoint of the line segments whose endpoints are given and (b) plot the endpoints and the midpoint on a rectangular coordinate system.$(-3,-3)$ and $(6,-1)$
In the following exercises, write the standard form of the equation of the circle with the given radius and center $(0,0)$,Radius: 7
In the following exercises, write the standard form of the equation of the circle with the given radius and center $(0,0)$,Radius: 9
In the following exercises, write the standard form of the equation of the circle with the given radius and center $(0,0)$,Radius: $\sqrt{2}$
In the following exercises, write the standard form of the equation of the circle with the given radius and center $(0,0)$,Radius: $\sqrt{5}$
In the following exercises, write the standard form of the equation of the circle with the given radius and centerRadius: 1, center: $(3,5)$
In the following exercises, write the standard form of the equation of the circle with the given radius and centerRadius: 10, center: $(-2,6)$
In the following exercises, write the standard form of the equation of the circle with the given radius and centerRadius: 2.5 , center: $(1.5,-3.5)$
In the following exercises, write the standard form of the equation of the circle with the given radius and centerRadius: 1.5 , center: $(-5.5,-6.5)$
For the following exercises, write the standard form of the equation of the circle with the given center with point on the circle.Center $(3,-2)$ with point $(3,6)$
For the following exercises, write the standard form of the equation of the circle with the given center with point on the circle.Center $(6,-6)$ with point $(2,-3)$
For the following exercises, write the standard form of the equation of the circle with the given center with point on the circle.Center $(4,4)$ with point $(2,2)$
For the following exercises, write the standard form of the equation of the circle with the given center with point on the circle.Center ( $-5,6$ ) with point ( $-2,3$ )
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x+5)^2+(y+3)^2=1$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x-2)^2+(y-3)^2=9$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x-4)^2+(y+2)^2=16$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x+2)^2+(y-5)^2=4$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$x^2+(y+2)^2=25$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x-1)^2+y^2=36$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x-1.5)^2+(y+2.5)^2=0.25$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$(x-1)^2+(y-3)^2=\frac{9}{4}$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$x^2+y^2=64$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$x^2+y^2=49$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$2 x^2+2 y^2=8$
In the following exercises, (a) find the center and radius, then (b) graph each circle.$6 x^2+6 y^2=216$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2+2 x+6 y+9=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2-6 x-8 y=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2-4 x+10 y-7=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2+12 x-14 y+21=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2+6 y+5=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2-10 y=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2+4 x=0$
In the following exercises, (a) identify the center and radius and (b) graph.$x^2+y^2-14 x+13=0$
Explain the relationship between the distance formula and the equation of a circle.
Is a circle a function? Explain why or why not.
In your own words, state the definition of a circle.
In your own words, explain the steps you would take to change the general form of the equation of a circle to the standard form.