The eccentricity of the locus of point `(2h+2,k),` where `(h , k)` lies on the circle `x^2+y^2=1` , is `1/3` (b) `(sqrt(2))/3` (c) `(2sqrt(2))/3` (d) `1/(sqrt(3))`

" The eccentricity of locus of point " (3h+2,k) " where " (h,k) " lies on the circle " x^(2)+y^(2)=1 " is."

The value of sin(1/4sin^(-1)(sqrt(63))/8) is 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

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 centre of a circle passing through (0,0),(1,0) and touching the Circle x^(2)+y^(2)=9 is a a ((1)/(2),sqrt(2)) b.((1)/(2),(3)/(sqrt(2))) c.((3)/(2),(1)/(sqrt(2))) d.((1)/(2),-(1)/(sqrt(2)))

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

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

If the area enclosed between the curves y=kx^(2) and x=ky^(2), where k>0, is 1 square unit.Then k is: (a) (1)/(sqrt(3)) (b) (sqrt(3))/(2) (c) (2)/(sqrt(3))(d)sqrt(3)

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

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

Let y=1/(2+1/(3+1/(2+1/(3+)))) , then the value of y is (a)(sqrt(13)+3)/2 (b) (sqrt(13)-3)/2 (c)(sqrt(15)+3)/2 (d) (sqrt(15)-3)/2