The normal at a point \(P\) on the parabola \(y^2=4ax\) meets the ellipse \(2x^2+y^2=c^2\) in the points \(M\), \(N\). Prove that \(P\) is the mid-point of \(MN\).

Hence, or otherwise, prove that the conics cut at right angles.

The normal at a point \(P\) on the parabola \(y^2=4ax\) meets the ellipse \(2x^2+y^2=c^2\) in the points \(M\), \(N\). Prove that \(P\) is the mid-point of \(MN\).

Hence, or otherwise, prove that the conics cut at right angles.