The equation of lines on which the perpendiculars from the origin make `30^0` angle with the x-axis and which form a triangle of area `(50)/(sqrt(3))` with the axes are (a) `sqrt(3)x+y-10=0` (b) `sqrt(3)x+y+10=0` (c)`x+sqrt(3)y-10=0` (d) `x-sqrt(3)y-10=0`

The equation of the line on which the perpendicular from the origin makes an angle of 30^@ with x - axis and which forms a triangle of area 50/sqrt3 with the axes is

The equation of a straight line on which the length of perpendicular from the origin is four units and the line makes an angle of 120^0 with the x-axis is (A) xsqrt(3)+y+8=0 (B) xsqrt(3)-y=8 (C) xsqrt(3)-y=8 (D) x-sqrt(3)y+8=0

The length of the perpendicular from origin to line is sqrt3x-y+24=0 is:

Find the equation of the straight line which passes through the origin and makes angle 60^0 with the line x+sqrt(3)y+sqrt(3)=0 .

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

Equation(s) of the straight line(s), inclined at 30^0 to the x-axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units, is (are) (a) x+sqrt(3)y+5sqrt(3)=0 (b) x-sqrt(3)y+5sqrt(3)=0 (c) x+sqrt(3)y-5sqrt(3)=0 (d) x-sqrt(3)y-5sqrt(3)=0

The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is (a) x^2+y^2+2sqrt(2)x+1=0 (b) x^2+y^2-2sqrt(3)y+2=0 (c) x^2+y^2+2sqrt(3)y+2=0 (d) x^2+y^2-2sqrt(2)+1=0

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 (a) sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

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)