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 .

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

The difference of the focal distances of any point on the hyperbola is equal to its

The locus ofthe foot of the perpendicular from the centre of the hyperbola

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

A point p is such that the sum of squares of its distance from the axes of coordinates is equal to the square of its distance from the line x-y=1. Find the locus of P