Condition on a & b so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by$

Asked Oct 01 '15 at 16:18

Active Oct 01 '15 at 16:18

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Find the condition on a & b so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by$

I tried finding the joint equation of tangents to the parabola $y^2=4ax$ like $SS_1=T^2$.Then I tried to apply the condition of normality to the joint pair of straight lines.But its becoming too huge.Please let me know if you can think of a shorter and more elegant method to prove $a^2>8b^2$.Thanks.

asked Oct 01 '15 at 16:18

Thanks a ton @labbhattacharjee...check this one too http://math.stackexchange.com/questions/1459857/condition-on-x-coordinate-of-a-point-such-that-three-distinct-normals-can-be-dra – Oct 01 '15 at 17:02
See https://www.google.im/advanced_search for exact search – lab bhattacharjee Oct 01 '15 at 17:04

Condition on a & b so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by$

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