Show that the lines `x^(2) - 4xy + y^(2) = 0` and `x + y = 10` contain the sides of an equilateral triangle.

Prove that lines 3x + y + 4 = 0, 3x + 4y = 20 and 24x - 7y + 5 = 0 are sides of an equilateral triangle.

Show that the line x^(2)-4xy+y^(2)=0 and x+y=3 from an equilateral triangle.

Show that the straight lines represented by 3x^(2)+48xy+23y^(2)=0 and 3x-2y+13=0 form an equilateral triangle of area (13)/(sqrt(3)) sq.units.

The equation of the in-circle of an equilateral triangle is x^(2) + y^(2) + 2x - 4y - 8 = 0 , find the area of the equilateral triangle.

Show that the straight line x^2-4xy+y^2=0 and x + y = 3 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.