Show that for rectangular hyperbola `xy=c^2`

The parametric form of rectangular hyperbola xy=c^(2)

If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2) , then

If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2) , then

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.

If PN is the perpendicular from a point on a rectangular hyperbola xy=c^(2) to its asymptotes,then find the locus of the midpoint of PN

Show that the normal to the rectangular hyperbola xy = c^(2) at the point t meets the curve again at a point t' such that t^(3)t' = - 1 .