If `S and S''` are the foci, C is the centre, and P is a point on a rectangular hyperbola, show that `SPxxS'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 ×S'P=(CP)^2

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

Statement 1 : Given the base B C of the triangle and the radius ratio of the excircle opposite to the angles Ba n dCdot Then the locus of the vertex A is a hyperbola. Statement 2 : |S P-S P|=2a , where Sa n dS ' are the two foci 2a is the length of the transvers axis, and P is any point on the hyperbola.

Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0) and (lambda,0) , the length of the transverse axis being 1 unit, then lambda can take the value 0 or 3. Statement 2 : |S^(prime)P-S P|=2a , where Sa n dS ' are the two foci, 2a is the length of the transverse axis, and P is any point on the hyperbola.

If S and T are foci of x^(2)/(16)-y^(2)/(9)=1 . If P is a point on the hyperbola then |SP-PT|=

Let S and S\' be the foci of the ellipse x^2/9 + y^2/4 = 1 and P and Q be points on the ellipse such that PS.PS\' is maximum and QS.QS \' is maximum. Statement 1 : PQ=4 . Statement 2 : If P is a point on an ellipse and S\' and S are its foci, then PS + PS\' is constant.

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)=p x^3+q x^2+r x+s ,then p+q+r+s= a. p b. -p c. 2p d. 0

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

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

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