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

The eccentricity of the hyperbola 4x^(2)-9y^(2) =36 is:

Which of the following can be slope of tangent to the hyperbola 4x^2-y^2=4? (a) 1 (b) -3 (c) 2 (d) -3/2

Find the coordinates of the foci and the center of the hyperbola, x^2-3y^2-4x=8

Find the eccentricity of the hyperbola with asymptotes 3x+4y=2 and 4x-3y=2 .

The eccentricity of the hyperbola 9x^(2) -4y^(2) + 36 = 0 is

The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the vertex A lies on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the side B C must touch parabola (b) circle hyperbola (d) ellipse

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

Let P(x, y) is a variable point such that |sqrt((x-1)^2+(y-2)^2)-sqrt((x-5)^2+(y-5)^2)|=3 , which represents hyperbola. The eccentricity e' of the corresponding conjugate hyperbola is (A) 5/3 (B) 4/3 (C) 5/4 (D) 3/sqrt7

Find the ratio of the eccentricities of the hyperbolas 2x^(2) - 3y^(2) = 1 and 3x^(2) - 2y^(2) = 1