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  • Let  be the ellipse <img alt="\mathrm{\frac{\mathrm{x}^{2}}{9}+\frac{\mathrm{y}^{2}}{4}=1}" src="

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

Option: 1

\mathrm{Q} lies inside \mathrm{C} but outside \mathrm{E}


Option: 2

\mathrm{Q}  lies outside both \mathrm{C} and \mathrm{E}


Option: 3

\mathrm{P}  lies inside both \mathrm{C} and \mathrm{E}


Option: 4

\mathrm{P} lies inside \mathrm{C} but outside \mathrm{E}


Answers (1)

\mathrm{1^{2}+2^{2}<9} and \mathrm{2^{2}+1<9} both \mathrm{P} and \mathrm{Q} lies inside \mathrm{C}.

\mathrm{Also \: \frac{1^{2}}{9}+\frac{2^{2}}{4}>1\: and \: \frac{2^{2}}{9}+\frac{1^{2}}{4}<1, P \: lies\: outside \: \mathrm{E}\: and \: \mathrm{Q}\: lies \: inside \: \mathrm{E}}.

\mathrm{\Rightarrow \mathrm{P}} lies inside \mathrm{\mathrm{C}} but outside \mathrm{\mathrm{E}}.

Posted by

Sumit Saini

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