Mathematics

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

consists of two parallel lines which are not coincident.

##### SOLUTION
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.

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Single Correct Medium Published on 09th 09, 2020
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