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 both C but outside E.
Correct Answer: D
Solution :
[d] Given equation of ellipse E is \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\] \[\Rightarrow \frac{4{{x}^{2}}+9{{y}^{2}}}{36}=1\Rightarrow 4{{x}^{2}}+9{{y}^{2}}=36\] \[\Rightarrow 4{{x}^{2}}+9{{y}^{2}}-36=0\] ?. (1) And C: Eqs of circle is \[{{x}^{2}}+{{y}^{2}}=9\] Which can be rewritten as \[{{x}^{2}}+{{y}^{2}}-9=0\] ? (2) For a point P (1, 2) we have \[4{{(1)}^{2}}+9{{(2)}^{2}}-36=40-36>0\] [from (1)] and \[{{1}^{2}}+{{2}^{2}}-9=5-9<0\] [from (2)] \[\therefore \] Point P lies outside of E and inside of C.
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