Question

The locus represented by the equation $x^2+y^2-2x-2y+2=(2x+y-3{)}^2$ is

• A. an ellipse
• B. a circle
• C. a pair of straight lines
• D. a hyperbola

Answer 1

The correct option is C a pair of straight lines

$(x-1{)}^2+(y-1{)}^2=(2x+y-3{)}^2$
Comparing and making it in form of $PS=e\left(PM\right)$
$\Rightarrow (x-1{)}^2+(y-1{)}^2=5{\left(\frac{2x+y-3}{\sqrt{5}}\right)}^2$
$\therefore$ Fixed point is $(1,1)$ and
Fixed line is $2x+y-3=0$
But $(1,1)$ lies on given line.
$\therefore$ Pair of straight lines