Thomas' Calculus 13th Edition

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. --- 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.