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The center of a circle is at [tex]\((-5, 2)\)[/tex] and its radius is 7.

What is the equation of the circle?

A. [tex]\((x + 5)^2 + (y - 2)^2 = 14\)[/tex]

B. [tex]\((x - 5)^2 + (y + 2)^2 = 14\)[/tex]

C. [tex]\((x - 5)^2 + (y + 2)^2 = 49\)[/tex]

D. [tex]\((x + 5)^2 + (y - 2)^2 = 49\)[/tex]

Sagot :

GinnyAnsweridn
To find the equation of a circle with a given center and radius, we use the standard form equation of a circle:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

Here, [tex]\((h, k)\)[/tex] represents the coordinates of the center of the circle, and [tex]\(r\)[/tex] represents the radius.

Given:
- The center of the circle is [tex]\((-5, 2)\)[/tex], so [tex]\(h = -5\)[/tex] and [tex]\(k = 2\)[/tex].
- The radius of the circle is [tex]\(7\)[/tex], so [tex]\(r = 7\)[/tex].

Substitute the values of [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:

[tex]\[ (x - (-5))^2 + (y - 2)^2 = 7^2 \][/tex]

Simplify the equation:

[tex]\[ (x + 5)^2 + (y - 2)^2 = 49 \][/tex]

Thus, the correct equation of the circle is:

[tex]\[ (x + 5)^2 + (y - 2)^2 = 49 \][/tex]

Among the given options, the correct choice is:

[tex]\[ (x + 5)^2 + (y - 2)^2 = 49 \][/tex]
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