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 \(x^2+ y^2= r^2\).

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

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

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