Question

Find the area bounded by the circle \[ x^2 + y^2 - 2x = 8. \]

Hint:

Rewrite equations of circles into standard form to identify key parameters like center and radius.

Answer 1

Rewritingtheequation: \[ x^2-2x+y^2=8\quad\Rightarrow\quad(x-1)^2+y^2=9. \] Thisrepresentsacirclecenteredat\((1,0)\)withradius\(r=3\).Theareaofthecircleis: \[ \text{Area}=\pir^2=\pi(3)^2=9\pi. \]