Put in parametric form, P1(2ap,ap2), P2(2a/p,a/p2). Since the tangent to the parabola at a point (2at,at2) has gradient t, the parameter at the point, and use point-gradient form, the equations of the tangents at P1 and P2 are y=px-ap2 and y=x/p-a/p2. Solve simultaneously, one obtains...