# The equation of a circle – Higher

Any point P with coordinates ( ) on the circumference of a circle can be joined to the centre (0, 0) by a straight line that forms the hypotenuse of a right angle triangle with sides of length and .

This means that, using Pythagoras’ theorem, the equation of a circle with radius and centre (0, 0) is given by the formula .

### Example

Find the equation of a circle with radius 3 units and centre (0, 0).

The radius, and , so the equation of the circle is .

### Example

What is the radius of the circle given by the equation ?

The value of so the radius of the circle is .