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 lines x^2-4xy+y^2=0 and x+y=3 form an equilateral triangle and find its area.

The angle between the straight lines 2x-y+3=0 and x+2y+3=0 is-

Show that the straight lines : x-y-1=0, 4x + 3y = 25 and 2x-3y + 1 = 0 are concurrent.

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Consider a pair of perpendicular straight lines 2x^2+3xy+by^2-11x+13y+c=0 The value fo c is

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a , b) (b) (b ,a) (-a ,-b) (d) none of these

If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

The lines given by the equation (2y^2+3xy-2x^2)(x+y-1)=0 form a triangle which is

Area of the triangle formed by the lines y=2x, y=3x and y=5 is equal to (in square units) :

Find the area of the triangle formed by the straight lines 7x-2y+10=0, 7x+2y-10=0 and 9x+y+2=0 (without sloving the vertices of the triangle).