Question

Let $S=\left\{(x,y)|x^2+2xy+y^2-3x-3y+2=0\right\}$, then $S-$

• A. consists of two coincident lines.
• B. consists of two parallel lines which are not coincident.
• C. consists of two intersecting lines.
• D. is a parabola.

Answer 1

The correct option is B consists of two parallel lines which are not coincident.

Given,

$x^2+2xy+y^2-3x-3y+2=0$

or, $(x+y{)}^2-3(x+y)+2=0$

or, $(x+y-2)(x+y-1)=0$.

or, $x+y=2$ and $x+y=1$ these are the straight lines represented by $S$ and these straight lines are parallel.