Rodriguez Coleman
03/17/2024 · Junior High School
Write an equation of the circle with center \( (-6,2) \) and diameter 4 . \( \square \)
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Step-by-step Solution
To write the equation of a circle, we can use the standard form of the equation of a circle, which 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.
Given the center of the circle \((-6, 2)\) and a diameter of 4, we can find the radius \(r\) by dividing the diameter by 2:
\[
r = \frac{4}{2} = 2
\]
Now we can substitute the center and the radius into the equation:
\[
(x - (-6))^2 + (y - 2)^2 = 2^2
\]
This simplifies to:
\[
(x + 6)^2 + (y - 2)^2 = 4
\]
Thus, the equation of the circle is:
\[
\boxed{(x + 6)^2 + (y - 2)^2 = 4}
\]
Quick Answer
The equation of the circle is \((x + 6)^2 + (y - 2)^2 = 4\).
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