Review question

# When do these normals to a parabola meet on the parabola? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9809

## Question

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

The parameters of the points $P$, $Q$ are $t_1$ and $t_2$ respectively. Show that, if $PQ$ passes through the point $(-2a,0)$, then $t_1t_2=2$ and the normals at $P$ and $Q$ to the parabola meet at a point $R$ on the parabola.

If $O$ is the origin, show, by considering the gradients of the sides of the quadrilateral $OPQR$ or otherwise, that the circumcircle of the triangle $PQR$ passes through $O$.