Answer
The unit circle.
Work Step by Step
The LHS can be written as $(x-0)^{2}+(y-0)^{2}$, which is the square of the distance of the point $(x,y)$ from the origin, $(0,0)$.
So, the distance of all these points from the origin
is equal to the square root of the RHS, which is 1.
This set of points is a circle, centered at the origin, with radius 1. We call this circle the unit circle.
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Alternatively, we could have compared the given equation to Equation (1) in the text
$(x-h)^{2}+(y-k)^{2}=r^{2}$
the standard equation for a circle of radius $r,$ centered at $(h,k)$, and arrived to the same answer: the unit circle.
