If a variable line has its intercepts on the coordinate axes `e and e^(prime),` where `e/2a n d e^(prime)/2` are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle `x^2+y^2=r^2,` where `r=`

The eccentricity of the hyperbola x^2-y^2=4 is

If e_1 and e_2 be the eccentricities of a hyperbola and its conjugate, show that 1/(e_1^2)+1/(e_2^2)=1 .

e_1 and e_2 are respectively the eccentricities of a hyperbola and its conjugate.Prove that 1/e_1^2+1/e_2^2=1

e_(1) and e_(2) are respectively the eccentricites of a hyperbola and its conjugate. Prove that (1)/(e_1^(2))+(1)/(e_2^2) =1

Find the point on the hyperbola x^2-9y^2=9 where the line 5x+12 y=9 touches it.

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is (a) 2 (b) 2sqrt(3) (c) 4 (d) 4/5

The pole of a straight line with respect to the circle x^2+y^2=a^2 lies on the circle x^2+y^2=9a^2 . If the straight line touches the circle x^2+y^2=r^2 , then :

If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

If radii of director circles of x^2/a^2+y^2/b^2=1 and x^2/a^2-y^2/b^2=1 are 2r and r respectively, let e_E and e_H are the eccentricities of ellipse and hyperbola respectively, then

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e_1a n de_2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that 1/(e_1^2)+1/(e_2^2)=2 .