The locus of a point whose chord of contact w.r.t. the hyperbola `x^2/a^2-y^2/b^2= 1` touches the circle in-scribed on the straight line joining the foci of the hyperbola `x^2/a^2-y^2/b^2=1` as diameter is

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

The locus of the point, whose chord of contact w.r.t the circle x^(2)+y^(2)=a^(2) makes an angle 2alpha at the centre of the circle is

The locus of the point, whose chord of contact w.r.t the circle x^(2)+y^(2)=a^(2) makes an angle 2alpha at the centre of the circle is

The equation of the chord of contact of the point (3,-2) w.r.t. the hyperbola 2x^(2) -3y^(2) =12 is

The locus of the point of intersection of tangents at the extremities of the chords of hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 which are tangents to the circle drawn on the line joining the foci as diameter is