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)=4ax 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 intercept made by the line sqrt2x-y-4sqrt2=0 on the parabola y^2=4x is equal to (a) 6sqrt3 (b) 4sqrt3 (c) 8sqrt2 (d) 6sqrt2

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)

The rationalisation factor of sqrt(3) is -sqrt(3) (b) (1)/(sqrt(3))(c)2sqrt(3)(d)-2sqrt(3)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The length of the chord y=sqrt3x-2sqrt3 intercepted by the parabola y^(2)=4(x-1) is equal to

The rationalisation factor of 2+sqrt(3) is 2-sqrt(3) (b) sqrt(2)+3(c)sqrt(2)-3(d)sqrt(3)-2

(2sqrt(27)-sqrt(75)+sqrt(12)) is equal to sqrt(3)(b)2sqrt(3) (c) 3sqrt(3)(d)4sqrt(3)

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) (4sqrt(2),2sqrt(2)) (b) (4sqrt(3),2sqrt(2)) (c) (4sqrt(3),2sqrt(3))( d) (4sqrt(2),2sqrt(3))

The length of latusrectum of the parabola 13[(x-3)^(2)+(y-4)^(2)]=(2x-3y+5)^(2) is A) (2)/(sqrt(13)) B) (4)/(sqrt(13)) C) (1)/(sqrt(13)) D) (5)/(sqrt(13))