Determine the center of the circle defined by the equation:
$(x-1)^{2}+(y+3)^{2}=4$

Answer

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Answer

Final Answer: The center of the circle is $\boxed{(1, -3)}$.

Steps

Step 1 ：The equation of a circle in standard form is $(x-h)^2 + (y-k)^2 = r^2$, where $(h, k)$ is the center of the circle and r is the radius.

Step 2 ：In the given equation, we can see that h = 1 and k = -3.

Step 3 ：Therefore, the center of the circle is $(1, -3)$.

Step 4 ：Final Answer: The center of the circle is $\boxed{(1, -3)}$.