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

Options

A. `(x^(2)-y^(2))^(2)=4x^(2)(x^(2)-a^(2))`
B. `(x^(2)-y^(2))^(2)=x^(2)(x^(2)-a^(2))`
C. `(x^(2)-y^(2))^(2)=4y^(2)(x^(2)-a^(2))`
D. `(x^(2)-y^(2))^(2)=y^(2)(x^(2)-a^(2))`

Answer

A