If a1a2=b1b2=c1c2 for a system of equations a1x+b1y+c1=0 and a2x+b2y+c2=0, then
Prove that the area of the parallelogram formed by the lines.
a1x+b1y+c1=0,a1x+b1y+d1=0,a2x+b2y+c2=0,a2x+b2y+d2=0 is ∣∣(d1−c1)(d2−c2)a1b2−a2b1∣∣ sq. units.
Deduce the condition for these lines to form a rhombus.