The parametric form of rectangular hyperbola `xy=c^2`

Show that for rectangular hyperbola xy=c^(2)

Locus of the middle points of the parallel chords with gradient m of the rectangular hyperbola xy=c^(2) is

IF xy =1 + sin ^(2) theta (thea is real parameter) be a family of rectangular hyperbolas and Delta is the area of the triangle formed by any tangent with coordinate axes, then

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.

The slope of the tangent to the rectangular hyperbola xy=c^(2) at the point (ct,(c)/(t)) is -

PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c^(2). If C is the center of the rectangular hyperbola,then find the value of product of the slopes of CP,CQ,CR, and CS.

At the point of intersection of the rectangular hyperbola xy=c^(2) and the parabola y^(2)=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi, respectively with x-axis,then