1.8Circles

x

y

(h, k)

r(x, y)

A circle is a set of points in the xy-plane that are a fixed distance r from a fixed point (h,k). The fixed distance is called the radius, and the fixed point (h,k) is called the center of the circle.

The standard form of an equation of a circle with radius r and center (h,k) is

Graph ( ) ( )x y 1 3 162 2

(-1,3)

(3,3)

(-1, 7)

(-5, 3)

(-1, -1)

x

y

The general form of the equation of a circle

Find the center and the radius of

First group terms:

Add appropriate terms to complete the squares for x and for y.