If the chords of the hyperbola x^2-y^2=a^2 touch the parabola y^2=4 a x . Then, the locus of the middle points of these chords is

Step-by-step solution

Equation of chord of hyperbola x^2-y^2=a^2 with mid-point as (h, k) is given by array rlrl & x h-y k & =h^2-k^2 y & = h k x- (h^2-k^2 ) k array This will touch the parabola y^2=4 a x , if aligned - ( h^2-k^2 k ) & = a h k a k^2 & =h^3+k^2 h aligned Locus of the mid-point is x^3=y^2(x-a)