A chord PQ of the hyperbola `xy=c^2` is tangent to the hyperbola `x^2 / a^2 - y^2 / b^2 = 1` Find the locus of the middle point of PQ.

P is a variable points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose vertex is A(a,0) The locus of the middle points AP is

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is: