Concyclic points on rectangular hyperbola

If P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3) and S(x_4, y_4) are 4 concyclic points on the rectangular hyperbola xy=c^(2) the coordinates of the orthocentre of the trianglePQR are

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

Prove that the tangent at any point on the rectangular hyperbola xy = c^2 , makes a triangle of constant area with coordinate axes.

The coordinates of a point on the rectangular hyperbola xy=c^(2) normal at which passes through the centre of the hyperbola are

A,B,C are three points on the rectangular hyperbola xy=c^(2), The area of the triangle formed by the tangents at A,B and C.