Prove that the lines `sqrt(3)x+y=0,\ sqrt(3)y+x=0,\ sqrt(3)x+y=1\ a n d\ sqrt(3)y+x=1` form a rhombus.

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

Find angles between the lines sqrt(3)x+y=1 and x+sqrt(3)y=1 .

Find angles between the lines sqrt(3)x+y=1 and x+sqrt(3)y=1 .

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

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

Prove that the lines y=sqrt3x+1,\ y=4\ n d\ y=-sqrt3x+2 form an equilateral triangle.

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

Solve the following system of equations: sqrt(2)x-sqrt(3)y=0,\ \ \ \ sqrt(3)x-sqrt(8)y=0

Solve the following system of equations: sqrt(2)x-sqrt(3)y=0,\ \ \ \ sqrt(3)x-sqrt(8)y=0

The graph of straight line y = sqrt(3)x + 2sqrt(3) is :