11. The curve \(C\) has parametric equations
$$x = 10 \cos 2 t , \quad y = 6 \sin t , \quad - \frac { \pi } { 2 } \leqslant t \leqslant \frac { \pi } { 2 }$$
The point \(A\) with coordinates \(( 5,3 )\) lies on \(C\).
- Find the value of \(t\) at the point \(A\).
- Show that an equation of the normal to \(C\) at \(A\) is
$$3 y = 10 x - 41$$
The normal to \(C\) at \(A\) cuts \(C\) again at the point \(B\).
- Find the exact coordinates of \(B\).