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

$\text{ Since }{1}^2+2^2=5<9\text{ and }{2}^2+1^2=5<9,\text{ both }P\text{ and }Q\text{ lie inside }C\text{ . Also, }$

$\frac{1^2}{9}+\frac{2^2}{4}=\frac{1}{9}+1>1\text{ and }\frac{2^2}{9}+\frac{1}{4}=\frac{25}{36}<1$

Hence, P lies outside E and Q lies inside E. 

Thus, P lies inside C but outside E.