Question

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

• A. square but not rhombus
• B. rhombus
• C. parallelogram
• D. rectangle but not a square

Answer 1

Answer: (C)

Given pair of lines are
$x^2-3xy+2y^2=0$
and $x^2-3xy+2y^2+x-2=0$
$\therefore \left(x-2y\right)\left(x-y\right)=0$
and $\left(x-2y+2\right)\left(x-y-1\right)=0$
$\Rightarrow x-2y=0,x-y=0$ and
$x-2y+2=0,x-y-1=0$
The lines $x-2y=0,x-2y+2=0$ and
$x-y=0,x-y-1=0$ are parallel.
Also, angle between $x-2y=0$ and
$x-y=0$ is not 90${}^{\circ }$.
$\therefore$ It is a parallelogram.