The pairs of straight lines `x^2-3xy+2y^2=0` and `x^2-3xy+2y^2+x-1` form a

Options

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

Answer

C

Explanation

Given pair of lines are `x^2-3xy+2y^2=0`
and `x^2-3xy+2y^2+x-2=0`
`therefore (x-2y)(x-y=0`
and `(x-2y+2)(x-y-1)=0`
`rArr x-2y=0,x-y=0`
and `x-2y+2=0,x-y-1=0`
Since 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^(@)`.
`therefore` it is a parallelogram.