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

Prove that the perpendicular bisectors of the sides of triangle are concurrent.

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

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

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

Prove that the diagonals of a square are equal.

If SY and S'Y' be drawn perpendiculars from foci to any tangent to a hyperbola. Prove that y and Y' lie on the auxiliary circle and that product of these perpendicular is constant.

Prove that the normal chord to a parabola at the point whose ordinate is equal to the abscissa subtends a right angle at the focus.

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

Statement I: The lines from the vertex to the two extremities of a focal chord of the parabola y^2=4ax are perpendicular to each other. Statement II: If the extremities of focal chord of a parabola are (at_1^2,2at_1) and (at_2^2,2at_2) , then t_1t_2=-1 .