Show that straight lines `(A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0` form with the line `A x+B y+C=0` an equilateral triangle of area `(C^2)/(sqrt(3(A^2+B^2)))` .

Show that straight lines (A^(2)-3B^(2))x^(2)+8ABxy+(B^(2)-3A^(2))y^(2)=0 form with the line Ax+By+C=0 an equilateral triangle of area (C^(2))/(sqrt(3(A^(2)+B^(2))))

Show that the straight lines (A^2-3B^2)x^2+ 8ABxy + (B^2-3A^2)y^2 = 0 form with the line Ax + By + C = 0 an equilateral triangle whose area is (C^2)/(sqrt3 (A^2+B^2))

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.

Show that the lines (x+2a)^2-3y^2=0,x=a form an equilateral triangle.

Show that the lines form an equilateral triangle and find its area (x+2a)^(2)-3y^(2)=0,x-a=0

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

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