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

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 eccentricity, centre, foci and vertices of the hyperbola 5x^(2)-4y^(2)=20 .

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

The eccentricity of the conic represented by x^2-y^2-4x+4y+16=0 is 1 (b) sqrt(2) (c) 2 (d) 1/2

The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 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 (a)parabola (b) circle (c)hyperbola (d) ellipse

The equation of conjugate axis of the hyperbola x y-3y-4x+7=0 is (a) y+x=3 (b) y+x=7 (c) y-x=3 (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

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

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