To find the equation of the circle given the center [tex]\((-3.2, -2.1)\)[/tex] and the radius 4.3, we use the standard form of the equation of a circle:
[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 [tex]\((h, k) = (-3.2, -2.1)\)[/tex]
- The radius [tex]\(r = 4.3\)[/tex]
We substitute these values into the standard form:
1. [tex]\(h = -3.2\)[/tex] and [tex]\(k = -2.1\)[/tex]
2. [tex]\(r = 4.3\)[/tex]
Thus, the equation becomes:
[tex]\[
(x - (-3.2))^2 + (y - (-2.1))^2 = (4.3)^2
\][/tex]
This simplifies to:
[tex]\[
(x + 3.2)^2 + (y + 2.1)^2 = 4.3^2
\][/tex]
Now, we match this equation to the given choices:
A. [tex]\((x+3.2)^2+(y-2.1)^2=4.3^2\)[/tex]
B. [tex]\((x-2.1)^2-(y+3.2)^2=(4.3)^2\)[/tex]
C. [tex]\((x+3.2)^2+(y+2.1)^2=(4.3)^2\)[/tex]
D. [tex]\((x+2.1)^2+(y-3.2)^2=4.3^2\)[/tex]
The correct equation that matches ours is:
C. [tex]\((x+3.2)^2+(y+2.1)^2=(4.3)^2\)[/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{3}
\][/tex]
