Rectangular hyperbola : `xy=c^2`

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) .

Hyperbola- Rectangular hyperbola

The length of the semi-transverse axis of the rectangular hyperbola xy=32 , is