8.
\includegraphics[max width=\textwidth, alt={}, center]{85427816-dcf1-49af-8d68-f4e88fc7d8f1-3_497_784_246_461}
The diagram shows the curve with parametric equations
$$x = - 1 + 4 \cos \theta , \quad y = 2 \sqrt { 2 } \sin \theta , \quad 0 \leq \theta < 2 \pi$$
The point \(P\) on the curve has coordinates \(( 1 , \sqrt { 6 } )\).
- Find the value of \(\theta\) at \(P\).
- Show that the normal to the curve at \(P\) passes through the origin.
- Find a cartesian equation for the curve.