Ramirez Medina
04/17/2023 · Middle School
Write the standard form of the equation of the circle of radius \( r=8 \) and center \( (h, k)=(0,0) \). The standard form of the equation of the circle is (Type an equation. Simplify your answer.)
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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:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given that the center is \((0, 0)\) and the radius \(r = 8\), we can substitute these values into the equation:
\[
(x - 0)^2 + (y - 0)^2 = 8^2
\]
This simplifies to:
\[
x^2 + y^2 = 64
\]
Thus, the standard form of the equation of the circle is:
\[
\boxed{x^2 + y^2 = 64}
\]
Quick Answer
\boxed{x^2 + y^2 = 64}
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