Three points E, F and G are taken on the parabola y²= 4ax, so that their ordinates (in order) are in geometric sequence. The ordinates of each of the three points have the same sign.

Do the tangents at E and G intersect on the line through F perpendicular to the axis of the parabola?

If this is always so, prove it. Otherwise, provide a counter example.

(In reply to re: A note about the problem. by Bractals)

Your E,F G do not form a geometric sequence.

F/E = -sqrt(k)
G/F = +sqrt(k)

Posted by Jer on 2013-02-03 19:40:35