On the parabola y^2=4ax, 3 points E,F,G are taken so that their ordinates are in G.P.

Question

Prove that the tangents at E and G intersect on the ordinate of F.

This was my approach:

Taking the three points as: E$(at_1^2,2at_1)$ , F$(at_2^2,2at_2)$, G$(at_3^2,2at_3)$
Using the G.P. condition and parametric coordinates, I was able to get: $t_1.t_3=t_2^2$

Also, as the point of intersection of tangents (genera formula for two points $(t_1),(t_2) $): $(at_1.t_2,a(t_1+t_2)$ :

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So, the point of intersection of tangents at E and G had the x-coordinate: $at_2^2$ (as $t_1.t_3 = t_2^2$)

But the question asks us to prove that it will have the same ordinate(y-coordinate) as that of point F... How can we get that conclusion?