Practice Equation of a Circle in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The standard form equation (x - h)^2 + (y - k)^2 = r^2 describes a circle with center (h, k) and radius r in the coordinate plane.

A circle is the set of all points at the same distance (the radius) from a center point. The equation just says 'the distance from (x, y) to the center (h, k) equals r,' using the distance formula squared.

Example 1

easy
Write the equation of the circle with center (3, -2) and radius 5.

Example 2

medium
Find the center and radius of the circle x^2 + y^2 - 6x + 4y - 12 = 0.

Example 3

medium
Find the equation of the circle that has a diameter with endpoints (-1, 4) and (5, -2).

Example 4

hard
Determine whether the circles (x-1)^2 + (y-3)^2 = 16 and (x-7)^2 + (y-3)^2 = 4 intersect, and find the number of intersection points.