A circle of radius \(r\) lies entirely in \(x>0,y>0\). The least distances from the circle to the \(x\)-axis and \(y\)-axis are 8 and 5 units respectively.

(a) State the centre in terms of \(r\). [1]

(b) The centre is 15 units from the origin. Find \(r\). [3]

(c) Point \(P\) is the point of the circle furthest from the origin. Find its tangent gradient. [2]