Equation of tangent of rectangular hyperbola

Equation of normal of rectangular hyperbola

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

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

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

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

The condition that a straight line with slope m will be normal to parabola y^(2)=4ax as well as a tangent to rectangular hyperbola x^(2)-y^(2)=a^(2) is