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

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is y-2at = -t(x-at^2) i.e. y=-tx+2at + at^3 Greatest and least distances between two curves occur along their common normals. Least and greatest distances of a point from a curve occur along the normal to the curve passing through that point. Shortest distance between parabola 2y^2-2x+1=0 and 2x^2-2y+1=0 is: (A) 1/2 (B) 1/sqrt(2) (C) 1/(2sqrt(2)) (D) 2sqrt(2)

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

The shortest distance between the parabola y^2 = 4x and the circle x^2 + y^2 + 6x - 12y + 20 = 0 is : (A) 0 (B) 1 (C) 4sqrt(2) -5 (D) 4sqrt(2) + 5

The shortest distance between line y"-"x""=""1 and curve x""=""y^2 is : (1) (sqrt(3))/4 (2) (3sqrt(2))/8 (3) 8/(3sqrt(2)) (4) 4/(sqrt(3))

The minimum vertical distance between the graphs of y=2+sinx and y=cosx is (a) 2 (b) 1 (c) sqrt(2) (d) 2-sqrt(2)

The distance between the parallel lnes y=2x+4 and 6x-3y-5 is (A) 1 (B) 17/sqrt(3) (C) 7sqrt(5)/15 (D) 3sqrt(5)/15

The area bounded between the parabolas x^2=y/4"and"x^2=9y and the straight line y""=""2 is (1) 20sqrt(2) (2) (10sqrt(2))/3 (3) (20sqrt(2))/3 (4) 10sqrt(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

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is a. sqrt(30) b. 2sqrt(30) c. 5sqrt(30) d. 3sqrt(30)