Review question

# 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

Ref: R5053

## Question

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 $p$.