For the hyperbola `x^2/100 - y^2/25 = 1`. prove that (i)eccentricity = 5/2(ii) `SA.S'A = 25`, where S & S' are the foci & A is the vertex

For the hyperbola x^2/100-y^2/25=1 , prove that SA*S'A=25 , where S and S' are the foci and A is the vertex.

In a rectangular hyperbola x^2-y^2=a^2 , prove that SP.S'P=CP^2 , where C is the centre and S, S' are the foci and P is any point on the hyperbola.

If S and S' are the foci and P be any point on the hyperbola x^(2) -y^(2) = a^(2) , prove that overline(SP) * overline(S'P) = CP^(2) , where C is the centre of the hyperbola .

If S, S' are the foci and' P any point on the rectangular hyperbola x^2 - y^2 =a^2 , prove that, bar(SP).bar(S'P) = CP^2 where C is the centre of the hyperbola

Eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 is

e is the eccentricity of the ellipse 4x^(2)+9y^(2)=36 and C is the centre and S is the focus and A is the vertex then CS:SA=

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.

If P is any point on the hyperbola x^(2)-y^(2)=a^(2) then S P . S^(prime) P=, where S, S^(prime) and C are respectively foci and the centre of the hyperbola

The eccentricity of the hyperbola x ^(2) - y^(2) =25 is