Let E be the ellipse $\frac{{\mathrm{x}}^2}{9}+\frac{{\mathrm{y}}^2}{4}=1$and C be the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=9$. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

$let E=\frac{x^2}{9}+\frac{y^2}{4}=1,C=x^2+y^2=9 and P=(1,2),Q=(2,1)$

since $1^2+2^2=5<9$ and $2^2+1^2=5<9$ both P and Q lie inside C.
Also $\frac{1^2}{9}+\frac{2^2}{4}=\frac{1}{9}+1>1\text{ and }\frac{2^2}{9}+\frac{1}{4}=\frac{25}{36}<1,\mathrm{P}$ lies outside E and Q lies inside E. Hence P lies inside C but outside E.