Question

Problems Set at an Oral Examination.
Represent the following sets of points on the plane (x, y).
$\left\{\right(x,y)|x^2+y^2-2x-2y+1=0\}.$

Answer 1

$x^2+y^2-2x-2y+1=0$

$⟹(x-1{)}^2+(y-1{)}^2=1$

This the equation of a circle of radius $1$ unit centered at $(1,1).$