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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.

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marked as duplicate by lab bhattacharjee, Community Oct 1 '15 at 17:04

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