How many normals to a parabola pass through $P$?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Find the equation of the normal to the parabola \(y^2=4ax\) at the point \((at^2,2at)\).

Prove that, if \(p^2>8\), two chords can be drawn through the point \((ap^2,2ap)\) which are normal to the parabola at their second points of intersection, and that the line joining these points of intersection meets the axis of the parabola in a fixed point, independent of \(p\).