The eccentricity of an ellipse whose pair of a conjugate diameter are `y=x` and `3y =-2x` is (A) `2/3` (B) `1/3` (C) `1/sqrt3` (D) none

The area bounded by the curve y^2=2x+1 and the line x-y=1 is (A) 2/3 (B) 8/3 (C) 16/3 (D) none of these

Find the eccentricity of the ellipse if y=x and 3y+2x=0 are the equations of a pair of its conjugate diameters.

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 area {(x,y) : |x| ge y ge x^2} is equal to (A) 1/12 (B) 1/6 (C) 1/3 (D) none of these

Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C) 1/3 (D) none of these

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

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

The eccentricity of an ellipse whose centre is at the origin is 1/2dot if one of its directrices is x=-4, then the equation of the normal to it at (1,3/2) is: (1) 4x+2y=7 (2) x+2y=4 (3) 2y-x=2 (4) 4x-2y=1

The eccentricity of the ellipse 25x^2+16 y^2=400 is a. 3//5 b. 1//3 c. 2//5 d. 1//5