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 asymptotes 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

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

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.

If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 and x - y = 0 then the orthocentre of the triangle lies on the line/lines

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) (1,-3/4) (2) (2,1/2) (3) (2,-1/2) (4) (1,3/4)

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

If four points be taken on a rectangular hyperbola such that the chord joining any two is perpendicular to the chord joining the other two, and if alpha,beta,gamma,delta be the inclinations to either asymptotes of the straight lines joining these points to the centre, then tanalphatanbetatangammatandelta is equal to

The focus of rectangular hyperbola (x-a)*(y-b)=c^2 is

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.