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.

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

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

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

If the tangent at any point P of a curve meets the axis of X in T find the curve for which O P=P T ,O being the origin.

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' 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 asymptotes is

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

If the tangent and normal to a rectangular hyperbola cut off intercepts a_(1) and a_(2) on one axis and b_(1) and b_(2) on the other, then

The equation of the line passing through the centre of a rectangular hyperbola is x-y-1=0 . If one of its asymptotoes is 3x-4y-6=0 , the equation of the other asymptote is