Equation of tangent of rectangular hyperbola

Equation of normal of rectangular hyperbola

Prove that the portion of the tangent of the rectangular hyperbola intercepted between the asymptotes is bisected at the point of contact and the area of the triangle formed by the tangent and the two asymptotes is constant.

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the rectangular hyperbola is

The vertices of triangleABC lie on a rectangular hyperbola such that the orhtocentre of the triangle is (2,3) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). Q. The equation of the rectangular hyperbola is

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

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: