Shortest distance between two parabolas `y^2 = x - 2` and ` x^2 = y-2` is : (A) `1/(4sqrt(2))` (B) `5/(4sqrt(2))` (C) `7/(2sqrt(2))` (D) `6/(7sqrt(2))`

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

The shortest distance between the line x=y and the curve y^(2)=x-2 is (a) 2 (b) (7)/(8) (c) (7)/(4sqrt(2)) (d) (11)/(4sqrt(2))

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)

7sqrt(2)x^(2)-10x-4sqrt(2)

The distance between the parallel planes x+2y-3z=2 and 2x+4y-6z+7=0 is (A) 1/sqrt(14) (B) 11/sqrt(56) (C) 7/sqrt(56) (D) none of these

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

consider a function f(x) Minimum distance between the functions f(x) and g(x) is (4)/(3sqrt(2)) (b) (7)/(6sqrt(2))( c) (7)/(3sqrt(2)) (d) (8)/(3sqrt(2))

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)