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A series of hyperbola are drawn having a...

A series of hyperbola are drawn having a common transverse axis of length 2a. Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote, is the curve `(x^2-y^2)^2 =lambda x^2 (x^2-a^2), ` then `lambda` equals

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