Question

The area (in $\text{sq.units}$) enclosed by the curve $|x^2+y^2+8y|<9$ is equal to

• A. $6\pi$
• B. $12\pi$
• C. $18\pi$
• D. $24\pi$

Answer 1

The correct option is C $18\pi$

Given curve : $|x^2+y^2+8y|<9$
$\Rightarrow |(x-0{)}^2+(y+4{)}^2-16|<9\Rightarrow -9<(x-0{)}^2+(y+4{)}^2-16<9\Rightarrow 7<(x-0{)}^2+(y+4{)}^2<25$
Which shows the region between two co-axial ring, of radius $\sqrt{7},5\text{units}.$

So. Required area $=\pi (5^2-7)=18\pi \text{sq.units}$