Question

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

• A. Q lies inside C but outside E
• B. Q lies outside both C & E
• C. P lies inside both C & E
• D. P lies inside C but outside E.

Answer 1

The correct option is D P lies inside C but outside E.

Since $1^2+2^2=5<9$

and $2^2+1^2=5<9$

both $P$ and $Q$ lies inside $C$

Also $\frac{1^2}{9}+\frac{2^2}{4}=\frac{1}{9}+1>1$ and

$\frac{2^2}{9}+\frac{1}{4}=\frac{16+9}{36}$

$=\frac{25}{36}<1$

$P$ lies outside $E$ and $Q$ lies inside $E$

Thus $P$ lies inside $C$ but outside $E$.