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.

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 four lines 3x + y = 0, 3y + x = 0, 3x + y = 4, 3y + x = 4 are at right angles.

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

The equation of the circumcircle of the triangle formed by the lines y + sqrt(3)x = 6, y - sqrt(3) x = 6 and y = 0 , is-

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

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

If the quadrilateral formed by the lines ax+by+c=0, 6sqrt(3)x+8sqrt(3)y+k=0 , ax+by+k=0 and 6sqrt(3)x + 8sqrt(3)y+c=0 has diagonals at right angles, then the value of a^2 +b^2 = …

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

Find the area of the closed figure bounded by the curves y=sqrt(x),y=sqrt(4-3x) and y=0

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