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 \(O\).
