Answer :
To find the equation of a circle given its center and radius, we'll use the standard form of the circle's equation:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
where:
- [tex]\((h, k)\)[/tex] are the coordinates of the center of the circle,
- [tex]\(r\)[/tex] is the radius of the circle.
Given:
- The center of the circle is [tex]\((-3.2, 2.1)\)[/tex], so [tex]\(h = -3.2\)[/tex] and [tex]\(k = 2.1\)[/tex].
- The radius of the circle is [tex]\(4.3\)[/tex], so [tex]\(r = 4.3\)[/tex].
Substitute [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:
[tex]\[ (x - (-3.2))^2 + (y - 2.1)^2 = (4.3)^2 \][/tex]
Simplify the terms in the equation:
[tex]\[ (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2 \][/tex]
This matches with choice C:
[tex]\[ (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2 \][/tex]
Thus, the correct answer is:
C. [tex]\((x + 3.2)^2 + (y - 2.1)^2 = 4.3^2\)[/tex]
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
where:
- [tex]\((h, k)\)[/tex] are the coordinates of the center of the circle,
- [tex]\(r\)[/tex] is the radius of the circle.
Given:
- The center of the circle is [tex]\((-3.2, 2.1)\)[/tex], so [tex]\(h = -3.2\)[/tex] and [tex]\(k = 2.1\)[/tex].
- The radius of the circle is [tex]\(4.3\)[/tex], so [tex]\(r = 4.3\)[/tex].
Substitute [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:
[tex]\[ (x - (-3.2))^2 + (y - 2.1)^2 = (4.3)^2 \][/tex]
Simplify the terms in the equation:
[tex]\[ (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2 \][/tex]
This matches with choice C:
[tex]\[ (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2 \][/tex]
Thus, the correct answer is:
C. [tex]\((x + 3.2)^2 + (y - 2.1)^2 = 4.3^2\)[/tex]
