The length of the chord of the parabola `y^2=x` which is bisected at the point (2, 1) is (a)`2sqrt(3)` (b) `4sqrt(3)` (c) `3sqrt(2)` (d) `2sqrt(5)`

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The length of the chord of the parabola x^(2) = 4y having equations x - sqrt(2) y + 4 sqrt(2) = 0 is

The value of cot70^0+4cos70^0 is (a) 1/(sqrt(3)) (b) sqrt(3) (c) 2sqrt(3) (d) 1/2

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis , then which of the following points lies on it: (a) (4sqrt2, 2sqrt2) (b) (4sqrt3, 2sqrt2) (c) (4sqrt3, 2sqrt3) (d) (4sqrt2, 2sqrt3)

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola y^2=4x above the x-axis is (a) sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

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

The largest value of a for which the circle x^2+y^2=a^2 falls totally in the interior of the parabola y^2=4(x+4) is (a) 4sqrt(3) (b) 4 (c) 4(sqrt(6))/7 (d) 2sqrt(3)

If the vertices of the parabola be at (-2,0) and (2,0) and one of the foci be at (-3,0) then which one of the following points does not lie on the hyperbola? (a) (-6, 2sqrt(10)) (b) (2sqrt6,5) (c) (4, sqrt(15)) (d) (6, 5sqrt2)

If two chords drawn from the point A(4,4) to the parabola x^2=4y are bisected by the line y=m x , the interval in which m lies is (-2sqrt(2),2sqrt(2)) (-oo,-sqrt(2))uu(sqrt(2),oo) (-oo,-2sqrt(2)-2)uu(2sqrt(2)-2,oo) none of these