If the distance between the foci and the distance between the two directricies of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` are in the ratio 3:2, then `b : a` is (a)`1:sqrt(2)` (b) `sqrt(3):sqrt(2)` (c)`1:2` (d) `2:1`

In an ellipse the distance between the foci is 8 and the distance between the directrices is 25. The length of major axis is : (A) 5sqrt(2) (B) 10sqrt(2) (C) 20sqrt(2) (D) none of these

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)

If distance between the foci of an ellipse is 6 and distance between its directrices is 12, then length of its latus rectum is : (A)4 (B) 3sqrt2 (C)9 (D) 2sqrt2

The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1 is ______

The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1 is ______

The distance between the origin and the tangent to the curve y=e^(2x)+x^2 drawn at the point x=0 is (a) (1/sqrt(5)) (b) (2/sqrt(5)) (c) (-(1)/sqrt(5)) (d) (2/sqrt(3))

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 foci of a hyperbola is 16 and its eccentricity is sqrt(2) then equation of the hyperbola is a. x^2+y^2=32 b. x^2-y^2=16 c. x^2+y^2=16 d. x^2-y^2=32

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these