circles

Definition

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

Standard Form of a Circle

Center is at (h, k)

(x-h)²+(y-k)² = r²

General Form of a Circle

Every binomial squared has been multiplied out.

Every term is on the left side, set equal to 0.

EX 1  Write the standard form for the equation of a circle with center (3, -2) and a radius of 4.

Converting from General Form to Standard

1. Move the x terms together and the y terms together.

2. Move C  to the other side.

3. Complete the square (as needed) for x.

4. Complete the square(as needed) for y.

5. Factor the left & simplify the right.