Prove that the parallelogram formed by the lines `x/a+y/b=1,x/b+y/a=1,x/a+y/b=2a n dx/b+y/a=2` is a rhombus.

The angle between the diagonals of a quadrilateral formed by the lines x/a+y/b=1,x/b+y/a=1,x/a+y/b=2 and x/b+y/a=2 is

Prove that the following sets of three lines are concurrent: x/a+y/b=1, x/b+y/a=1\ a n d\ y=x

Prove that the area of the parallelogram formed by the lines a_1x+b_1y+c_1=0,a_1x+b_1y+d_1=0,a_2x+b_2y+c_2=0, a_2x+b_2y+d_2=0, is |((d_1-c_1)(d_2-c_2))/(a_1b_2-a_2b_1)| sq. units.

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

Show that the tangent of an angle between the lines x/a+y/b=1 and x/a-y/b=1\ i s(2a b)/(a^2-b^2)

Straight lines (x)/(a)+(y)/(b)=1, (x)/(b)+(y)/(a)=1,(x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 form a rhombus of area ( in square units)

Show that the parallelogram formed by ax+by+c=0, a_1 x+ b_1 y+c=0, ax+by+c_1 =0 and a_1 x+b_1 y+c_1 =0 will be a rhombus if a^2 +b^2 = (a_1)^2 + (b_1)^2 .

Prove that the line x/a + y/b =1 and x/b - y/a =1 are perpendicular to each other.

Prove that the lines 2x-3y+1=0,\ x+y=3,\ 2x-3y=2\ a n d\ x+y=4 form a parallelogram.

Show that the tangent of an angle between the lines (x)/(a)+(y)/(b)=1 and (x)/(a)-(y)/(b)=1 and (2ab)/(a^(2)-b^(2)) .