# Equation of a Circle

This page looks at equations of a circle and completing the square.

The equation of a circle with centre (a, b) and radius r is (x - a)^{2} + (y - b)^{2} = r^{2}.

This is a result of Pythagoras' Theorem

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For example, the equation of a circle with centre (3, 0) and radius 4 units is (x – 3)^{2} + y^{2} = 16.

The General Form of the equation of a circle is x^{2} + y^{2} + 2gx +2fy + c = 0.

The centre of the circle is (-g, -f) and the radius is √(g^{2} + f^{2 } - c).

**Completing the square**

Given a circle in the general form you can complete the square to change it into the standard form.

More on this can be found on the Quadratic Equations page Here.

**Circle Properties**

You need to remember circle properties found Here