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

Prove that the eccentricity of a rectangular hyperbola is equal to sqrt2 .

P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot

The eccentricity of a rectangular hyperbola, is

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

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

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 PG to a curve meets the x-axis in G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.