Problem

The hyperbola $H$ has Cartesian equation $xy = 25$

The parabola $P$ has parametric equations $x = 10t^2$, $y = 20t$

The hyperbola $H$ intersects the parabola $P$ at the point $A$

(a) Use algebra to determine the coordinates of $A$

The point $B$ with coordinates $(10, 20)$ lies on $P$

(b) Find an equation for the normal to $P$ at $B$

Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers to be determined.

(c) Use algebra to determine, in simplest form, the exact coordinates of the points where this normal intersects the hyperbola $H$