Problem

Three points $P$, $Q$ and $R$ have coordinates $P(-13, 5)$, $Q(5, 1)$ and $R(2, k)$, where $k$ is a constant. It is given that the angle $PRQ$ is a right angle.

(a) Show that one of the possible values of $k$ is 10, and find the other possible value.

(b) It is now given that $k = 10$. A circle passes through the points $P$, $Q$ and $R$.

Find the equation of the tangent to the circle at $R$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.