The equation of a circle – Higher

Any point P with coordinates ( x,~y) 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 x and y.

This means that, using Pythagoras’ theorem, the equation of a circle with radius r and centre (0, 0) is given by the formula x^2+ y^2= r^2.

Diagram showing Find the equation of a circle with radius 3 units and centre (0, 0) The radius, r = 3 and r^2 = 9, so the equation of the circle is x^2 + y^2 = 9

Example

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

The radius, r = 3 and r^2 = 9, so the equation of the circle is x^2 + y^2 = 9.

Example

What is the radius of the circle given by the equation x^2 + y^2 = 15?

The value of r^2 = 15 so the radius of the circle is \sqrt{15}.