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

Show that the lines x^2-4xy+y^2=0 and x+y=1 form an equilateral triangle and find its area.

Prove that the lines 2x-3y+1=0,\ x+y=3,\ 2x-3y=2\ a n d\ x+y=4 form a parallelogram.

Show that the straight lines x^2+4xy+y^2=0 and the line x-y=4 form an equilateral triangle .

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.

P is a point on the line y+2x=1, and Q and R are two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

Statement - 1 : Equations (2 pm sqrt3) x - y = 1 pm 2sqrt3 represent two sides of an equilateral triangle having one vertex (2 , 3) and x + y - 2 = 0 as the opposite side . Statement - 2 : The equation of the lines passing through (x_(1) , y_(1)) and making constant angle alpha with the line y = mx + c are given by y - y_(1) = (m pm tan alpha)/( 1 pm tan alpha) ( x - x_(1))

The angle between lines y=(2-sqrt(3))x+5 and y=(2+sqrt(3))x+7 is

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 .