An ellipse of semi-axes a, b slides betw...

An ellipse of semi-axes `a, b` slides between two perpendiuclar lines. Prove that the locus of its foci is `(x^2 + y^2) (x^2 y^2 + b^4) = 4a^2 x^2 y^2`, the two lines being taken as the axes of coordinates.

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