If `Sa n dS '` are the foci, `C` is the center, and `P` is a point on a rectangular hyperbola, show that `S PxxS^(prime)P=(C P)^2dot`

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)

Show that for rectangular hyperbola xy=c^(2)

The fouce of the rectangular hyperbola (x-h) (y-k) =p^(2) is

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

The vertex of the rectangular hyperbola (x-h)(y-k)=p^(2) is

If p,q,r,s are rational numbers and the roots of f(x)=0 are eccentricities of a parabola and a rectangular hyperbola,where f(x)=px^(3)+qx^(2)+rx+s, then p+q+r+s= a.p b.-p c.2p d.0

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= d_1: d_2 (b) d_2: d_1 d1 2:d2 2 (d) sqrt(d_1):sqrt(d_2)