Two lines drawn at right angles, one being a tangent to $y^2=4ax$ and the other to $x^2=4by$. Find the locus of their point of intersection.

Question

sasogeek · Answer

is this like one of those challenge questions?

anonymous · Answer

It ain't challenge question, I have already solved it but I need a better way.

dumbcow · Answer

sorry for not posting any work.
here is what i came up with, 
Let c be any given x on the curve x^2 =4by
Then the point of intersection of tangent line at c with perpendicular tangent line is (x*,y*):
$$x^{*} = \frac{c^{2}(c-2a)}{2(c^{2}+4b^{2})}$$
$$y^{*} = \frac{-c(a+2b^{2}c)}{2b(c^{2}+4b^{2})}$$