Algebra II Recipe: Writing an Equation of a Circle Given Its Center and a Point on the Circle

Writing an equation

Use

Substitute the values of the center in place of h and k.

Substitute the values of the center of the circle in place of x and y.

Simplify the expression to find r (the radius).

Substitute the radius value into x² + y² = r² when the center is (0,0).

Substitute the radius and center (h, k) into (x - h)² + (y - k)² = r² when the center is NOT (0,0).

Examples:

Write the equation of the circle with center (0,0) and (5,1) is a point on the circle.

Write the equation of the circle with center (-2,3) and (3,3) is a point on the circle.