The lines `(lx+my)^2-3(mx-ly)^2=0` and `lx+my+n=0` forms

Prove that the line lx+my+n=0 and the pair of lines (lx+my)^2-3(mx-ly)^2=0 form an equilateral triangle and its area is (n^2)/(sqrt(3)(l^2+m^2))

Find the area (in square units) of the quadrilateral formed by the two pairs of lines l^2x^2-m^2y^2-n(lx+my)=0 and l^2x^2-m^2y^2+ n(lx-my) = 0

The lines lx+my+n=0,mx+ny+l=0 and nx+ly+m=0 are concurrent if (where l!=m!=n)

Show that the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent if l+m+n=0

The circumcentre of the triangle formed by the lines x+y=0, x-y=0 and lx+my=1 is

If the lines lx + my + n = 0, mx + ny + l = 0 and nx + ly + m = 0 are concurrent then

The area (in square units ) of the quadrilateral formed by two pairs of lines l^(2) x^(2) - m^(2) y^(2) - n (lx + my) = 0 and l^(2) x^(2)- m^(2) y^(2) + n (lx - my ) = 0 , is

The area (in square units ) of the quadrilateral formed by two pairs of lines l^(2) x^(2) - m^(2) y^(2) - n (lx + my) = 0 and l^(2) x^(2)- m^(2) y^(2) + n (lx - my ) = 0 , is