Finding the points that distance from a specefic point

Question

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

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$(x-1)^2 + (y-1)^2 = 9$

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$x^2 -2x +1 +y^2 -2y + 1 = 9$

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$x^2-2x+y^2-2y=7$

and i'm stuck in here, how can i continue?

Answer 1

Of course it is a circle, and $(x-1)^2+(y-1)^2=9$ is it's equation.

Hence, $$(X,Y)\in \mathcal{C}_{(c,r)},\quad c=(1,1),\ r=3$$