In a rectangular hyperbola, prove that
SP. S'P = `CP^(2)`.

If SandS' are the foci,C is the center,and P is a point on a rectangular hyperbola,show that SP xx S'P=(CP)^(2)

If S ans S' are the foci,C is the center,and P is point on the rectangular hyperbola,show that SP xx SP=(CP)^(2)

If P is any point on the hyperbola whose axis are equal,prove that SP.S'P=CP^(2).

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.

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

From a point P, tangents are drawn to the hyperbola 2xy = a^(2) . If the chord of contact of these tangents touches the rectangular hyperbola x^(2) - y^(2) = a^(2) , prove that the locus of P is the conjugate hyperbola of the second hyperbola.

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of (SN)/(SP).