Question

The area bounded by the circles $x^2+y^2=4,$ $x^2+y^2=16$ and the two rays given by $2x^2-3xy-2y^2=0(y\ge 0)$ is

• A. $3\pi$ sq. unit
• B. $\frac{3\pi }{2}$ sq. unit
• C. $6\pi$ sq. unit
• D. $\frac{3\pi }{4}$ sq. unit

Answer 1

The correct option is A $3\pi$ sq. unit

Given circles : $x^2+y^2=2^2$ and $x^2+y^2=4^2$
Given rays : $2x^2-3xy-2y^2=0(y\ge 0)$
Here, coefficient of $x^2$ $+$ coefficient of $y^2=0$
$\therefore$ Both lines are perpendicular and also pass through the origin.


Hence, required area
$=\frac{1}{4}\times \pi (4^2-2^2)=3\pi$ sq. unit