To determine the correct equation representing a circle with a given center and radius, we need to recall the standard form of the equation of a circle.
The standard form of the equation of a circle is:
[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.
Given:
- The center of the circle is [tex]\((-5, 5)\)[/tex], so [tex]\(h = -5\)[/tex] and [tex]\(k = 5\)[/tex].
- The radius [tex]\(r\)[/tex] is 3 units.
We substitute [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:
[tex]\[
(x - (-5))^2 + (y - 5)^2 = 3^2
\][/tex]
Simplifying the terms, we get:
[tex]\[
(x + 5)^2 + (y - 5)^2 = 9
\][/tex]
Thus, the equation of the circle with center at [tex]\((-5, 5)\)[/tex] and radius 3 units is:
[tex]\[
(x + 5)^2 + (y - 5)^2 = 9
\][/tex]
Therefore, the correct answer is:
[tex]\[ A. \ (x+5)^2+(y-5)^2=9 \][/tex]
