A) Q lies inside C but outside E
B) Q lies outside both C and E
C) P lies inside both C and E
D) P lies inside C but outside E
Correct Answer: D
Solution :
The given ellipse is \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\]. The value of the expression \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}-1\] is positive for \[x=1,\,y=2\] and negative for \[x=2,\,y=1\]. Therefore P lies outside E and Q lies inside E. The value of the expression \[{{x}^{2}}+{{y}^{2}}-9\]is negative for both the points P and Q. Therefore P and Q both lie inside C. Hence P lies inside C but outside E.
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