Locus of the mid-point of the chord of the hyperbola x2a2-y2b2=1 which is a tangent to the circle x2+y2=c2  is

Let (h, k) be the mid-point of the chord, then its equation ishxa2-kyb2=h2a2-k2b2Since it touches the circle x2+y2=c2h2a2-k2b2ha22+kb22=±c⇒h2a2-k2b22=c2h2a4+k2b4Required locus is x2a2-y2b22=c2x2a4+y2b4