I have to find the set of points $(X,Y)$
that have a distance of $3$ from the point $(1,1)$
i thought of it as a circle, so i did the distance formula and this is what i got
$\sqrt{(x-1)^2 +(y-1)^2 } = 3$
i squared both sides
and i got
$(x-1)^2 + (y-1)^2 = 9$
$x^2 -2x +1 +y^2 -2y + 1 = 9$
$x^2-2x+y^2-2y=7$
and i'm stuck in here, how can i continue?
Of course it is a circle, and $(x-1)^2+(y-1)^2=9$ is it's equation.
Hence, $$(X,Y)\in \mathcal{C}_{(c,r)},\quad c=(1,1),\ r=3$$