Rectangular hyperbola : `xy=c^2`

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola and xy = c^2 , then find coordinates of the orthocentre of the triangle PQR

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

If (x_(1),y_(1)),Q(x_(2),y_(2)),R(x_(3),y_(3)) and S(x_(4),y_(4)) are four concyclic points on the rectangular hyperbola ) and xy=c^(2), then coordinates of the orthocentre ofthe triangle PQR is

The tangent at the point P on the rectangular hyperbola xy=k^(2) with C intersects the coordinate axes at Q and R. Locus of the coordinate axes at triangle CQR is x^(2)+y^(2)=2k^(2)(b)x^(2)+y^(2)=k^(2)xy=k^(2)(d) None of these

Find the length of that focal chord of the parabola y^(2) = 4ax , which touches the rectangular hyperbola 2xy = a^(2) .