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
easyWrite the equation of the circle with center (3, -2) and radius 5.
Example 2
mediumFind the center and radius of the circle x^2 + y^2 - 6x + 4y - 12 = 0.
Example 3
mediumFind the equation of the circle that has a diameter with endpoints (-1, 4) and (5, -2).
Example 4
hardDetermine 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.