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(2): A note about the problem. by Jer)

You are looking at the x coordinates, not the y coordinates.

Posted by Bractals on 2013-02-04 13:37:43