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 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 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 pair of asymptotes is

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

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.

The vertices of a triangle have integer co- ordinates then the triangle cannot be

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

The vertices of a triangle are at the vertices of an octagon. The number of such triangles are

Let k be an integer such that the triangle with vertices (k ,-3k),(5, k) and (-k ,2) has area 28s qdot units. Then the orthocentre of this triangle is at the point : (1,-3/4) (2) (2,1/2) (3) (2,-1/2) (4) (1,3/4)

Two vertices of a triangle are (5,-1) and (-2,3) If the orthocentre of the triangle is the origin, find the coordinates of the third point.

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.