Deleon Ortiz
06/19/2023 · High School
Write the standard equation of the circle with center \( (-3,-8) \) and \( r=\sqrt{5} \). (Type an equation. Simplify your answer.) (Type is form of the equation of the circle is
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The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is \((x - h)^2 + (y - k)^2 = r^2\).
Given that the center of the circle is \((-3, -8)\) and the radius is \(\sqrt{5}\), we can substitute these values into the standard form equation to find the equation of the circle.
Substitute \(h = -3\), \(k = -8\), and \(r = \sqrt{5}\) into the standard form equation:
\((x - (-3))^2 + (y - (-8))^2 = (\sqrt{5})^2\)
Simplify the equation:
\((x + 3)^2 + (y + 8)^2 = 5\)
Therefore, the standard equation of the circle with center \((-3, -8)\) and radius \(\sqrt{5}\) is \((x + 3)^2 + (y + 8)^2 = 5\).
Quick Answer
\((x + 3)^2 + (y + 8)^2 = 5\)
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