If C is the centre of a hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , S, S its foci and P a point on it. Prove tha SP. S'P `=CP^2-a^2+b^2`

If P(theta) is a point on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , whose foci are S and S', then SP.S'P =

Let 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^2).

A tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its asymptotes at P and Q. If C its centre,prove that CP.CQ=a^(2)+b^(2)

if S and S are two foci of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ( altb ) and P(x_(1) , y_(1)) a point on it then SP+ S'P is equal to

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=

If P is a point on the rectangular hyperbola x^(2)-y^(2)=a^(2),C is its centre and S,S ,are the two foci,then the product (SP.S'P)=