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

If a+b=2h, then the area of the triangle formed by the lines ax^(2)+2hxy+by^(2)=0 and the line x-y+2=0, in sq.units is

If the straight lines 2x+3y-1=0,x+2y-1=0, andax +by-1=0 form a triangle with the origin as orthocentre,then (a,b) is given by (a) (6,4) (b) (-3,3)( c) (-8,8) (d) (0,7)

Show that |a b c a+2x b+2y c+2z x y z|=0

Area of triangle formed by straight lines 3x - y = 3, x - 2y + 4 =0 and y =0 is