In a rectangular hyperbola, prove that CP and CD are equal, and are inclined to the axis at a angles which are complementary.

Find the angle which is three times of its complementary angle.

In a rectangular hyperbola, prove that the product of the focal distances of a point on it is equal to the square of its distance from the centre of the hyperbola .

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

Which angle is two third of its complementary angle?

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

If angle subtended by any chord of a rectangular hyperbola at the centre is alpha and angle between the tangents at ends of chord is beta , then

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.

The axis of earth's magnetic field is inclined with the geographical axis at an angle of about :