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 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

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

If the area of the triangle formed by the pair of lines 8x^(2)-6xy+y^(2)=0 and the line 2x+3y=a is 7 then a=

Area of the triangle formed by the lines 2x-y=6 and 3x^(2)-4xy+y^(2)=0 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)