Question

If the normal at t1 and t2 intersects the curve again at t3 then prove that the line joining t1 and t2 always passes through a fixed point (-2a,0)​

Answer 1

Answer:

If the normals to the parabola y^2 = 4ax at the points t1 & t2 intersect again on the parabola at the point ‘t3’ then t1*t2 = 2 ; t3 = – (t1 + t2) and hence prove that the line joining t1 & t2 passes through a fixed point (–2a, 0).