Owen Dawson
07/22/2023 · Middle School
Write the standard form of the equation of the circle with its center at \( (-7,0) \), and a radius of 10 .
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Step-by-step Solution
The standard form of 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 \((-7, 0)\) (where \(h = -7\) and \(k = 0\)), and the radius is \(10\) (so \(r = 10\)).
Now, we can substitute these values into the standard form equation:
\[
(x - (-7))^2 + (y - 0)^2 = 10^2
\]
This simplifies to:
\[
(x + 7)^2 + y^2 = 100
\]
Thus, the standard form of the equation of the circle is:
\[
(x + 7)^2 + y^2 = 100
\]
Quick Answer
The standard form of the equation of the circle is \((x + 7)^2 + y^2 = 100\).
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