Question 6 - A-Level Maths

$$x ^ { 2 } + y ^ { 2 } + 8 x - 4 y = 0$$

Find
1. the coordinates of the centre of $C$,
2. the exact radius of $C$. The point $P$ lies on $C$.
  Given that the tangent to $C$ at $P$ has equation $x + 2 y + 10 = 0$
find the coordinates of $P$
Find the equation of the normal to $C$ at $P$, giving your answer in the form $y = m x + c$ where $m$ and $c$ are integers to be found.