Question 6 - A-Level Maths

The rectangular hyperbola $H$ has equation $x y = 25$
1. Verify that, for $t \neq 0$, the point $P \left( 5 t , \frac { 5 } { t } \right)$ is a general point on $H$.
The point $A$ on $H$ has parameter $t = \frac { 1 } { 2 }$
Show that the normal to $H$ at the point $A$ has equation $$8 y - 2 x - 75 = 0$$ This normal at $A$ meets $H$ again at the point $B$.
Find the coordinates of $B$.
\includegraphics[max width=\textwidth, alt={}, center]{38217fcb-8f26-49ac-9bb1-61c2f304006e-13_2261_50_312_36}
VIAV SIHI NI BIIIM ION OC VGHV SIHI NI GHIYM ION OC VJ4V SIHI NI JIIYM ION OC