All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: A note about the problem. | Comment 3 of 6 |

`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 thegeometric sequence. The intersection of the tangent lines topoints E and G would have an y coordinatethat is less than zero.`

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

 Search: Search body:
Forums (0)