# What is the standard form of an equation of a circle? Definition and examples

The standard form of an equation of a circle with center (h,k) and radius r is (x - h)^{2} + (y - k)^{2} = r^{2}

If you put the center at the origin of the coordinate system, the standard form of the equation of the circle is x^{2} + y^{2} = r^{2}

## How to write the standard form of an equation of a circle

Write an equation of a circle with center (-2, 5) and radius 3

(x - h)^{2} + (y - k)^{2} = r^{2}

Substitute 3 for r, -2 for h, and 5 for k

(x - -2)^{2} + (y - 5)^{2} = 3^{2}

Simplify

(x + 2)^{2} + (y - 5)^{2} = 9

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