Unit 8B: Equation of a Circle Review

Given: Circle P with center at (-2, 3) and a radius of  $\sqrt{23}$  . Identify the equation that could represent circle P. 

•  $\left(x-2\right)^2+\left(y-3\right)^2=23$  

•  $\left(x-2\right)^2+\left(y+3\right)^2=23$  

•  $\left(x+2\right)^2+\left(y-3\right)^2=23$  

•  $\left(x+2\right)^2+\left(y+3\right)^2=23$  

Circle O has a center at (1,-3) and a diameter of 8 units. Identify which point lies on Circle O.

• (-6, 5)

• (5, -3)

• (1, 5)

• (-2, -4)

The equation  $\left(x-5\right)^2+\left(y-1\right)^2=r^2$  represents circle A. The point (9, -2) lies on the circle. What is r, the length of the radius of circle A? 

•  $1$  

•  $5$  

•  $4\sqrt{3}$  

•  $\sqrt{17}$  

A circle has a center of (8, -3) and a radius of 2 units. Select the three parts that would create the equation of this circle.

•  $\left(y-3\right)^2$  

•  $\left(y+3\right)^2$  

•  $2^2$  

•  $\left(x-8\right)^2$  

•  $\left(x+8\right)^2$  
  

Which point lies on the circle represented by the equation  $\left(x-6\right)^2+\left(y-1\right)^2=4^2$  ?

• (4, 3)

• (10, 0)

• (6, 1)

• (2, 1)

Given: Circle P has a center at (4, -4)

Given: (1, 0) is a point on the circle

Determine the diameter of circle P?

• 5 units

• 4 units

• 10 units

• 12 units

The endpoints of the diameter for a circle are (3, -5) and (-1, 7). What is the length of the radius. Round to the nearest tenth (one decimal place!).

Identify the center of the circle defined by the equation  $\left(x-8\right)^2+\left(y+3\right)^{2\ }=9^2$  

Identify the description that matches this equation.  $x^2+y^2=49$  

• a circle with center (0, 0) and radius 7

• a circle with center (1, 1) and radius 7

• a circle with center (0, 0) and radius 49

• a circle with center (0, 0) and radius 1

Which point does not lie on the circle with center (0, 0) and radius 6?

• (-6, 0)

• (6, 0)

• (0, 6)

• (6, -6)