Question:
Find the area bounded by the circle
\[
x^2 + y^2 - 2x = 8.
\]
Find the area bounded by the circle
\[
x^2 + y^2 - 2x = 8.
\]
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Rewrite equations of circles into standard form to identify key parameters like center and radius.
Updated On: Mar 1, 2025
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Solution and Explanation
Rewritingtheequation:
\[
x^2-2x+y^2=8\quad\Rightarrow\quad(x-1)^2+y^2=9.
\]
Thisrepresentsacirclecenteredat\((1,0)\)withradius\(r=3\).Theareaofthecircleis:
\[
\text{Area}=\pir^2=\pi(3)^2=9\pi.
\]
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