Barker Schwartz
06/26/2024 · Primary School
Write an equation of the circle with center \( (3,8) \) and radius 7.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
The equation of a circle with center \((h, k)\) and radius \(r\) is given by the formula:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((3, 8)\) and the radius is \(7\). Plugging these values into the formula, we have:
- \(h = 3\)
- \(k = 8\)
- \(r = 7\)
Now substituting these values into the equation:
\[
(x - 3)^2 + (y - 8)^2 = 7^2
\]
Calculating \(7^2\):
\[
7^2 = 49
\]
Thus, the equation of the circle is:
\[
(x - 3)^2 + (y - 8)^2 = 49
\]
Quick Answer
The equation of the circle is \((x - 3)^2 + (y - 8)^2 = 49\).
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