Equation of a Circle

Equation of a Circle

Finding (h,k) and r

•  $\left(x-h\right)^2+\left(y-k\right)^2=r^2$ 

•  $\left(x-6\right)^2+\left(y-1\right)^2=9$  

• h = 6, k = 1 --> center: (6, 1)

• r =  $\sqrt{9}=3$  

Multiple Choice

Find the center: $\left(x+4\right)^2+\left(y-2\right)^2\ =\ 25$ 

• (4, 2)

• (-4, -2)

• (-4, 2)

• (4, -2)

Multiple Choice

Find the radius: $\left(x+4\right)^2+\left(y-2\right)^2\ =\ 25$  

• 2.5

• 5

• 25

• 50

Multiple Choice

Find the center: $\left(x-7\right)^2+y^2\ =\ 25$  

• (7, 0)

• (-7, 0)

• (7, 1)

• (-7, -1)

Multiple Choice

Find the diameter: $\left(x-3\right)^2+\left(y+1\right)^2=49$  

• 3.5

• 7

• 14

• 49

Multiple Choice

 $x^2+\left(y+10\right)^2=42.25$  Find the center:

• (0, 10)

• (0, -10)

• (1, 10)

• (1, -10)

Writing the Equation

•  $\left(x-h\right)^2+\left(y-k\right)^2=r^2$  

• Find the center (h, k): (3, -2)

• Find the radius (count): r = 5
  

• Fill in for h, k and r:

•  $\left(x-3\right)^2+\left(y+2\right)^2=25$  

Multiple Choice

What is the equation of the circle?

center: (5, 3), radius: 2

• $\left(x-5\right)^2+\left(y-3\right)^2=2$

• $\left(x-5\right)^2+\left(y-3\right)^2=4$

• $\left(x+5\right)^2+\left(y+3\right)^2=2$

• $\left(x+5\right)^2+\left(y+3\right)^2=4$

Multiple Choice

What is the equation of the circle?

center: (0, -3), radius: 5

•  $x^2+\left(y+3\right)^2=2.5$ 

•  $x^2+\left(y-3\right)^2=5$ 

•  $x^2+\left(y+3\right)^2=25$ 

•  $x^2+\left(y-3\right)^2=25$ 

Multiple Choice

What is the equation of the circle?

center: (4, 0), diameter: 6

•  $\left(x-4\right)^2+y^2=9$ 

•  $\left(x+4\right)^2+y^2=9$ 

•  $\left(x-4\right)^2+y^2=36$ 

•  $\left(x+4\right)^2+y^2=36$