A triangle has its vertices on a rectangular hyperbola. Prove that the orthocentre of the triangle also lies on the same hyperbola.

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 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 number of real tangents that can be drawn from the point (1, 1) to the rectangular hyperbola is

The eccentricity of a rectangular hyperbola, is

If abscissa of orthocentre of a triangle inscribed in a rectangular hyperbola xy=4 is (1)/(2) , then the ordinate of orthocentre of triangle is

Prove that the eccentricity of a rectangular hyperbola is equal to sqrt2 .

The normal at three points P, Q, R on a rectangular hyperbola intersect at a point T on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

Tangents are drawn to the parabola at three distinct points. Prove that these tangent lines always make a triangle and that the locus of the orthocentre of the triangle is the directrix of the parabola.

Show that the orthocentre of a triangle whose vertices lie on the hyperbola xy = c^(2) , also lies on the same hyperbola.

If a rectangular hyperbola circumscribes a triangle, show that the curve passes through the orthocentre of the triangle. Find the distances from A(4, 2) to the points in which the line 3x-5y=2 meets the hyperbola xy=24 .

A, B, C are three points on the rectangular hyperbola xy = c^2 , The area of the triangle formed by the points A, B and C is