(a)[4]
Point $P$ travels along the curve so that its $y$-coordinate is falling at $5$ units per second. Find how fast the $x$-coordinate of point $P$ is rising when $y = 32$.
(b)[6]
The $y$-coordinate of point $A$ on the curve is 32. At point $B$ on the curve, the gradient of the curve is $-3$. Find the equation of the perpendicular bisector of $AB$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.