perplexus.info :: Geometry : Geometric Parabola

Geometric Parabola (Posted on 2013-02-02)

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Yes! The tangents at E and G will always intersect on the line through F perpendicular to the axis of the parabola!!
For an explanation, refer to the calculus solution submitted by Jer in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(4): A note about the problem.	Jer	2013-02-04 16:25:40
re(3): A note about the problem.	Bractals	2013-02-04 13:37:43
re(2): A note about the problem.	Jer	2013-02-03 19:40:35
re: A note about the problem.	Bractals	2013-02-03 15:50:03
A note about the problem.	Jer	2013-02-03 01:17:48
Calculus solution	Jer	2013-02-03 01:12:43

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