The eccentricity of the hyperbola `x=a/2(t+1/t), y=a/2(t-1/t)` is a.`sqrt(2)` . b. `sqrt(3)` c. `2sqrt(3)` d. `3sqrt(2)`

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

The distance between the directrices of the hyperbola x=8s e ctheta,\ y=8\ t a ntheta, a. 8sqrt(2) b. 16sqrt(2) c. 4sqrt(2) d. 6sqrt(2)

The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 , is

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). (a) sqrt(3) (b) sqrt(3)+1 (c) ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is a. 1/(sqrt(2)) b. sqrt(2/3) c. sqrt(3/2) d. none of these

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 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 conic x=3((1-t^(2))/(1+t^(2))) and y=(2t)/(1+t^(2)) is