Find common tangent of the two curve `y^(2)=4x` and `x^(2)+y^(2)-6x=0` (a) `y=(x)/(3)+3` (b) `y=((x)/(sqrt(3))-sqrt(3))` (c) `y=(x)/(3)-3` (d) `y=((x)/(sqrt(3))+sqrt(3))`

The gradient of the common tangent to the two curves y=x^2-5x+6 and y=x^2+x+1 is: -1/3 (b) -2/3 (c) -1 (d) -3

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) find x^2+y^2

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , find x^2+y^2

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , find x^2+y^2

If 5-sqrt(3)=x+y sqrt(3) then (x,y) is

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola y^2=4x above the x-axis is sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C) 1/3 (D) none of these

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

Find the angle between the lines y-sqrt(3)x-5=0 and sqrt(3)y-x+6=0 .