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 ×S'P=(CP)^2

If P is any point on the hyperbola whose axis are equal, prove that S PdotS^(prime)P=C P^2dot

If Sa n dS ' are two foci of ellipse 16 x^2+25 y^2=400 and P S Q is a focal chord such that S P=16 , then find S^(prime)Qdot

If Sa n dS ' are two foci of ellipse 16 x^2+25 y^2=400a n dP S Q is a focal chord such that S P=16 , then find S^(prime)Qdot

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^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 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

In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >2P S