How do you find the centre and radius of a circle using the equation of a circle?

The equation of a circle is a wonderful way to display information about the circle itself.

Let's look below at an example of a circle equation in its proper form:

In order to find the centre of the circle, we simply look at the values within the brackets. The centre in this case would be (2, 4) .

The radius is the square root of the right hand side of the equation. In this case it would be r = 4.

More generally, From the standard equation of a circle (x−a)^2 + (y−b)^2 = r^2, the center is the point (a,b) and the radius is r.