Question

Points A,B and C lie on the parabola y² = 4ax. The tangents to the parabola at A,B and C, taken in pairs, intersect at points P,Q and R. Determine the ratio of the areas of the triangle ABC and PQR.

Answer 1

Let the three points on the parabola be 

Equation of the tangent to the parabola at (at², 2at ) is

ty = x + at² 

Therefore, equations of tangents at A and B are