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

The curve xy=c(c>0) and the circle x^(2)+y^(2)=1 touch at two points,then distance between the points of contact is

The shortest distance between the point (0, 1/2) and the curve x = sqrt(y) , (y gt 0 ) , is:

The slope of the tangent to the curve y=sqrt(4-x^(2)) at the point where the ordinate and the abscissa are equal is -1 (b) 1 (c) 0 (d) none of these

Parabola y^(2)=4a(x-c_(1)) and x^(2)=4a(y-c_(2)), where c_(1) and c_(2) are variable,are such that they touch each other. The locus of their point of contact is xy=2a^(2) (b) xy=4a^(2)xy=a^(2)(d) none of these

If the line y=x+sqrt(3) touches the ellipse (x^(2))/(4)+(y^(2))/(1)=1 then the point of contact is

The distance of the point P(a ,\ b ,\ c) from the x-axis is a. sqrt(b^2+c^2) b. sqrt(a^2+c^2) c. sqrt(a^2+b^2) d. none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a)x+3y=2 (b) x+2y=2( c) x+y=2 (d) none of these

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 angle of intersection between the curves, y=x^2 and y^2 = 4x , at the point (0, 0) is (A) pi/2 (B) 0 (C) pi (D) none of these