Equation of normal of rectangular hyperbola

Equation of tangent of rectangular hyperbola

What are the degree and order respectively of differential equation of the family of rectangular hyperbolas whose axis of symmetry are the coordinate axis ?

Equation of the rectangular hyperbola whose focus is (1,-1) and the corresponding directrix is x-y+1=0

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 .

The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola,is

If for a rectangular hyperbola a focus is (1,2) and the corresponding directrix is x+y=1 then the equation of the rectangular hyperbola is