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)`

Find the maximum vertical distance between the graphs y=2+3sinx and y=4cos x-3 .

The distance between the graphs of the equations y=-1\ a n d\ y=3 is: (a) 2 (b) 4 (c) 3 (d) 1

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)

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

Draw the graph of y= sqrt (x^(2)-1)

Draw the graph of y= -sqrt(x^(2)+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 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 curve x y=c ,(c >0), and the circle x^2+y^2=1 touch at two points. Then the distance between the point of contacts is 1 (b) 2 (c) 2sqrt(2) (d) none of these