Question

For the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ and circle $(x-1{)}^2+(y+2{)}^2=3,$ the centre of the circle lies

• A. inside the ellipse
• B. outside the ellipse
• C. on the ellipse
• D. none of these

Answer 1

The correct option is B outside the ellipse

Centre of the circle is $(1,-2)$
we have,
$S_1=\frac{1}{4}+\frac{4}{1}-1>0$
$\Rightarrow$ The centre of the circle lies outside the ellipse