The eccentricity of ellipse `ax^2 + by^2 + 2gx + 2fy + c = 0` if its axis is parallel to x-axis is (A) `sqrt((a+b)/(4)` (B) `sqrt((a-b)/(2)` (C) `sqrt((b-a)/(a)` (D) `sqrt((b-a)/(b)`

If : asec^(2) theta - b * tan^(2) theta = c,"then" = sin theta = A) sqrt((a +c)/(b + c) B) sqrt((a -c)/(b - c) C) sqrt((a -c)/(b + c) D) sqrt((a + c)/(b - c)

(sqrt8)^(1/3) = ? (a) 2 (b) 4 (c) sqrt2 (d) 2sqrt2

The shortest distance of the point (a,b,c) from x-axis (A) sqrt(a^2+b^2) (B) sqrt(b^2+c^2) (C) sqrt(c^2+a^2) (D) sqrt(a^2+b^2+c^2)

a((sqrt(a)+sqrt(b))/(2b sqrt(a)))^(-1)+b((sqrt(a)+sqrt(b))/(2a sqrt(b)))^(-1)

Distance of the points (a,b,c) for the y axis is (a) sqrt(b^(2)+c^(2)) (b) sqrt(c^(2)+a^(2)) (c )sqrt(a^(2)+b^(2)) (d) sqrt(a^(2)+b^(2)+c^(2))

sqrt(a/b+b/a-2)= 1) sqrt(a/b)+sqrt(b/a) 2) sqrt(a/b)-sqrt(b/a) 3) sqrt(a)/b-b/sqrt(a) 4) sqrt(a)/b-sqrt(b)/a

(a+c sqrt(b))(2+y sqrt(b))

The length of perpendicular from the centre to any tangent of the ellipse x^2/a^2 + y^2/b^2 =1 which makes equal angles with the axes, is : (A) a^2 (B) b^2 (C) sqrt(a^2-b^2)/2) (D) sqrt((a^2 + b^2)/2)

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

If : a * cos A-b * sin A=c, "then" : a * sin A +b* cos A= A) sqrt(a^(2)+b^(2)-c^(2)) B) sqrt(a^(2)-b^(2)+c^(2)) C) sqrt(b^(2)+c^(2)-a^(2)) D) sqrt(b^(2)+c^(2)+a^(2))