The general equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$

Here, $(h, k)$ represents the center of the circle, and $r$ is the radius. If the given equation is written as:

$(x + 2)^2 + (y - 3)^2 = r^2$

we can rewrite $x + 2$ as $x - (-2)$, indicating that $h = -2$, and $y - 3$ remains as $y - k$, meaning $k = 3$.

Thus, the center of the circle is:

$(-2, 3)$

The correct answer is:

(-2, 3)

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Related Questions:

1. How is the radius of a circle determined from its equation?
2. What is the equation of a circle centered at $(4, -5)$ with radius 6?
3. How can the equation of a circle be rewritten if expanded into general form?
4. How do we find the center if the circle equation is written in general form?
5. What happens if the circle is shifted along the axes?

Tip:

When dealing with circle equations, always look for terms in the form $(x-h)^2 + (y-k)^2$. These directly reveal the center.