6. The rectangular hyperbola \(H\) has equation \(x y = 25\)
- 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 \(B\).