SAT Question fc8aa563: Circles answer and explanation with Desmos solution

Choice C is correct. The equation of a circle in the xy-plane can be written as $(x-h{)}^2+(y-k{)}^2=r^2$, where the center of the circle is $(h,k)$ and the radius of the circle is $r$. It's given that the circle in the xy-plane is defined by the equation $(x-1{)}^2+(y+7{)}^2=1$. This equation can be written as $(x-1{)}^2+(y-(-7){)}^2=1$. For this equation, it follows that $h=1$ and $k=-7$. Therefore, the center of the circle in the xy-plane defined by the given equation is $(1,-7)$.