Three points E, F and G are chosen on the parabola y² = 4ax such that their y-coordinates form a geometric progression. The point where the tangents at E and G meet lies on the

Question

Accepted Answer

vertical line through F. For y^2=4ax with points at parameters t1,t2, tangents meet at (a*t1*t2, a(t1+t2)). y-coords in GP means t_E,t_F,t_G in GP, so t_E*t_G = t_F^2. The intersection x-coordinate a*t_E*t_G = a*t_F^2 equals F's x-coordinate, so the meeting point lies on the vertical line through F.

Three points E, F and G are chosen on the parabola y² = 4ax such that their y-coordinates form a geometric progression. The point where the tangents at E and G meet lies on the

Solution

Related JEE Main Maths questions