Question 1092598
The first circle is centered at (0,0) with a radius of 1.
Complete the square to find the center and radius of the second circle.
{{{x^2+(y^2-2y)=8}}}
{{{x^2+(y^2-2y+1)=8+1}}}
{{{x^2+(y-1)^2=9}}}
So the second circle is centered at (0,1) with a radius of 3.
So the first circle is completely contained in the second.
Use the circle area formula to get the answer,
{{{A=pi*R[2]^2-pi*R[1]*2}}}
{{{A=pi*(3)^2-pi*(1)^2}}}
{{{A=pi(9-1)}}}
{{{A=8pi}}}