The vertices of  △ABC  on a rectangular hyperbola such that the orthocentre of triangle is  (3, 2)  and the asymptotes of the rectangular hyperbola are parallel to co-ordinate axes. The two perpendicular tangent intersect at  (1, 1) .The equation of an asymptotes is

The equation of the asymptotes of a rectangular hyperbola, which are parallel to the coordinate axes, is given by y = ±x.

Since the asymptotes are parallel to the coordinate axes, the center of the hyperbola is at the origin (0,0).

The equation of the hyperbola is x² - y² = a².

The orthocenter of the triangle is given as (3,2). This point lies on the hyperbola, so it satisfies the equation of the hyperbola. Substituting x = 3 and y = 2 into the equation of the hyperbola gives 9 - 4 = a², so a² = 5.

The point of intersection of the tangents is given as (1,1). This point also lies on the hyperbola, so it satisfies the equation of the hyperbola. Substituting x = 1 and y = 1 into the equation of the hyperbola gives 1 - 1 = a², so a² = 0.

Since a² cannot be both 5 and 0, there is a contradiction. Therefore, the given conditions cannot all be satisfied by a single hyperbola.