2. The ellipse \(E\) has equation
$$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$$
The line \(l\) is the normal to \(E\) at the point \(P ( 6 \cos \theta , 5 \sin \theta )\), where \(0 < \theta < \frac { \pi } { 2 }\)
- Use calculus to show that an equation of \(l\) is
$$6 x \sin \theta - 5 y \cos \theta = 11 \sin \theta \cos \theta$$
The line \(l\) meets the \(x\)-axis at the point \(Q\).
The point \(R\) is the foot of the perpendicular from \(P\) to the \(x\)-axis.
- Show that \(\frac { O Q } { O R } = e ^ { 2 }\), where \(e\) is the eccentricity of the ellipse \(E\).