To write the equation of a circle, we use the standard formula:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In your case, the center of the circle is \((-3, 2)\), which means \(h = -3\) and \(k = 2\). The radius \(r\) is given as \(2\). Therefore, \(r^2 = 2^2 = 4\).
Plugging in the values into the formula, we have:
\[ (x - (-3))^2 + (y - 2)^2 = 4 \]
This simplifies to:
\[ (x + 3)^2 + (y - 2)^2 = 4 \]
So, the correct equation for the circle is:
\[ (x + 3)^2 + (y - 2)^2 = 4 \]
Thus, the correct option from your list is:
(x + 3)² + (y − 2)² = 4.
2 answers