The ration in which the line segement joining the points `(4,-6)` and `(3,1)` is divided by the parabola `y^2=4x` is (a)`(-20+-sqrt(155))/(11):1` (b) `(-20+-sqrt(155))/(11):2` (c)`-20+-2sqrt(155): 11` (d) `-20+-sqrt(155): 11`

The equation of the line joining the points (-3,4,11) and (1,-2,7) is

The length of projection of the line segment joining the points (1,0,-1)a n d(-1,2,2) on the plane x+3y-5z=6 is equal to a. 2 b. sqrt((271)/(53)) c. sqrt((472)/(31)) d. sqrt((474)/(35))

The length of projection of the line segment joining the points (1,0,-1)a n d(-1,2,2) on the plane x+3y-5z=6 is equal to a. 2 b. sqrt((271)/(53)) c. sqrt((472)/(31)) d. sqrt((474)/(35))

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)

The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is 2sqrt(2) (b) 1/2sqrt(2) (c) 4 (d) sqrt((36)/5)

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)

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

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

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 the tangent drawn at point (t^2,2t) on the parabola y^2=4x is the same as the normal drawn at point (sqrt(5)costheta,2sintheta) on the ellipse 4x^2+5y^2=20, then theta=cos^(-1)(-1/(sqrt(5))) (b) theta=cos^(-1)(1/(sqrt(5))) t=-2/(sqrt(5)) (d) t=-1/(sqrt(5))