Prove that the diagonals of the parallelogram formed by the four lines `3x + y = 0, 3y + x = 0, 3x + y = 4, 3y + x = 4` are at right angles.

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

The triangle formed by the lines x + y = 0,3x + y = 4,x+3y = 4 is

The equation of the diagonal of the square formed by the pairs of lines xy +4x - 3y - 12 = 0 and xy - 3x +4 y - 12 = 0 is

If the area of the parallelogram formed by the lines 2x - 3y + a = 0 , 3x - 2y - a = 0 , 2x - 3y + 3a = 0 and 3x - 2y - 2a = 0 is 10 square units , then a =

Prove that the area of the parallelogram contained by the lines 4y-3x-a=0,3y-4x+a=0,4y-3x-3a=0, and 3y-4x+2a=0 is (2/7)a^2dot

Prove that the area of the parallelogram contained by the lines 4y-3x-a=0,3y-4x+a=0,4y-3x-3a=0, and 3y-4x+2a=0 is (2/7)a^2dot

The equation of the diagonal through origin of the quadrilateral formed by the lines x = 0, y = 0, x + y - 1 = 0 and 6x + y - 3= 0, is

Find the area of the triangle formed by the lines y+x-6=0, 3y-x+2=0 and 3y=5x+2 .

Find the area of the parallelogram formed by the lines 2x^2+5xy+3y^2=0 and 2x^2+5xy+3y^2+3x+4y+1=0

The diagonals of a parallelogram PQRS are along the lines x+3y =4 and 6x-2y = 7, Then PQRS must be :