Turnbull Knight
01/24/2023 · Junior High School
Write an equation of the circle with center \( (-7,-3) \) and radius 6
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Tutor-Verified Answer
Step-by-step Solution
The equation of a circle in standard form is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For a circle with center \((-7, -3)\) and radius \(6\):
- \(h = -7\)
- \(k = -3\)
- \(r = 6\)
Now, substituting these values into the equation:
\[
(x - (-7))^2 + (y - (-3))^2 = 6^2
\]
This simplifies to:
\[
(x + 7)^2 + (y + 3)^2 = 36
\]
Thus, the equation of the circle is:
\[
(x + 7)^2 + (y + 3)^2 = 36
\]
Quick Answer
The equation of the circle is \((x + 7)^2 + (y + 3)^2 = 36\).
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