6.2 Equations of Circles Practice

Which equation of a circle is centered at (-3, 2) and has a radius of 5?

• (x + 3)² + (y - 2)² = 25

• (x - 3)² + (y + 2)² = 5

• (x + 3)² + (y - 2)² = 5

• (x - 3)² + (y + 2)² = 25

Which graph corresponds to

(x+2)²+ (y-3)²=36

• A

• B

• C

• D

Plot the circles x² + y² = 4 and x² + y² = 1 on the same coordinate plane.

Match each equation to its description.

• Circle centered at (0, -4) and radius 3

• (x – 1)² + y² = 9

• Circle centered at (1, 0) and radius 3

• (x – 1)² + (y + 4)² = 9

• Circle centered at (1, 4) and radius √3

• (x – 1)² + (y – 4)² = 3

• Circle centered at (1, -4) and radius √3

• x² + (y + 4)² = 9

• Circle centered at (1, -4) and radius 3

• (x – 1)² + (y + 4)² = 3

Match each quadratic expression with an equivalent expression in factored form.

• (x+4)(x+2)

• x²+6x+9

• (x+7)(x-1)

• x²+6x-7

• (x+1)(x+5)

• x²+6x

• (x+3)(x+3)

• x²+6x+5

• x(x+6)

• x²+6x+8

Match the following

• (x + 8)²

• x² + 8x + 16 =

• (x - 8)²

• x² + 16x + 64 =
• (x + 4)²

• x² + 4x + 4 =

• (x -2)²

• x² - 16x + 64 =

• (x + 2)²

• x² - 4x + 4 =

An equation of a circle is x² - 8x + 16 + y² + 10y + 25 = 81.

What is the radius of the circle?

Mathematical Equivalence

ON

An equation of a circle is x² - 8x + 16 + y² + 10y + 25 = 81

What is the center of the circle?

• (4, 5)
• (4, -5)
• (4, -10)
• (2, -5)

Complete the Square:

x² + 14x + ____

x² - 18x + (a)   = (x -​ (b)   )²​

• 81
• 18
• 27
• 9
• 3
• 1
• 36