G.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Example Problems

The center of the circle is

(30, -40)

.

The equation of a circle is given below.

(x + 4)^{2} + (y - 11)^{2} = 64

What is its center?

The equation of a circle is given below.

(x + 13)^{2} + (y - 1)^{2} = 10

What is its center?

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