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Geometric Parabola (Posted on 2013-02-02) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: A note about the problem. | Comment 3 of 6 |
(In reply to A note about the problem. by Jer)

With your parabola y = x^2, what about points
   E = (-sqrt(b),b)
   F = (sqrt(k*b),k*b)
   G = (k*sqrt(b),k^2*b)
with k,b > 0. The y coordinates form the
geometric sequence.
The intersection of the tangent lines to
points E and G would have an y coordinate
that is less than zero.

  Posted by Bractals on 2013-02-03 15:50:03
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