For real numbers a ,   b a > b > 0 , let Area x ,   y : x 2 + y 2 ≤ a 2 and x 2 a 2…

We know that area of circle $={\mathrm{\pi r}}^2$ ($r$ is radius of circle) and area of ellipse $=\mathrm{\pi ab}$ (where $a \& b$ are length of semi major and semi minor axis)

Now given area between circle and ellipse  $\Rightarrow \pi a^2-\pi ab=30\pi$  .....(i)

And $\Rightarrow \pi ab-\pi b^2=18\pi$ ....(ii)

On subtracting equation (i) - (ii), we get ${\left(a-b\right)}^2=a^2-2ab+b^2=12$.