13. The point \(A ( 9 , - 13 )\) lies on a circle \(C\) with centre the origin and radius \(r\).
- Find the exact value of \(r\).
- Find an equation of the circle \(C\).
A straight line through point \(A\) has equation \(2 y + 3 x = k\), where \(k\) is a constant.
- Find the value of \(k\).
This straight line cuts the circle again at the point \(B\).
- Find the exact coordinates of point \(B\).