To determine the equation of a circle given its center and radius, we use the standard form of the circle equation:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Here, we are given:
- The center of the circle [tex]\((h, k)\)[/tex] is [tex]\((4, -3)\)[/tex]
- The radius [tex]\(r\)[/tex] is [tex]\(3\)[/tex]
Substituting these values into the standard form equation, we have:
[tex]\[
(x - 4)^2 + (y + 3)^2 = 3^2
\][/tex]
Therefore, the equation of the circle is:
[tex]\[
(x - 4)^2 + (y + 3)^2 = 3^2
\][/tex]
Looking at the provided options, the correct answer is:
D. [tex]\((x - 4)^2 + (y + 3)^2 = 3^2\)[/tex]
