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.

Find the orthocenter of the triangle formed by the lines x + 2y = 0, 4x + 3y - 5 =0, 3x + y = 0 .

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

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 in square units , is

Prove that the diagonals of the parallelogram formed by the four lines : (x)/(a)+(y)/(b)=1 , (x)/(a)+(y)/(b)=-1 , (x)/(a)-(y)/(b)=1 , (x)/(a)-(y)/(b)=-1 are at right angles.

Show that the area of the parallelogram formed by the lines x+3y-a = 0 , 3x-2y+3a=0, x + 3y +4a = 0 and 3x + 2y + 7a = 0 is 20/11 a^(2) sq units/

The area of the parallelogram formed by the lines 3x+4y=7a;3x+4y=7b;4x+3y-7c and 4x+3y=7d is-

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^(2)

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

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