How to Find the Equation of a Circle

Description

A detailed tutorial on how to find the equation of a circle. Step by step tutorial including several examples of how to find the equation of a circle for reference.

Overview

The equation of a circle is really the distance from the point (h, k) – the center of the circle – to the point (x, y) – a point somewhere on the outside of the circle. This distance will be called r. Having this information, we can now insert it into the distance formula:

r = sqrt[(x - h)^2 + (y - k)^2]

But because no one wants to solve a square root, we can simplify the formula and get rid of the square root entirely:

r^2 = (x – h)^2 + (y – k)^2

This is the general formula for a circle. You must always have the center and radius of a circle to be able to solve. However, even if you are not given these you can easily find them by using the distance and midpoint formulas with whatever points you are given.