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Let E be d ellipse x(sq)/9 + y(sq)/4=1 an C be d circle x(sq)+y(sq)=9. Let P an Q be d pts (1,2) an (2,1) resp. Then (a) Q lies inside C but outside E. (b) Q lies outside C an E. (c) P lies inside both C an E. (d) P lies inside C but outside E. ANSWER:- (d) P lies inside C but outside E. SOLUTION:- For the ellipse, x2/ a2 + y2/ b2 = 1--------eq1 the auxiliary circle is x2 + y2 = a2 ---------eq2 It is known that the ellipse lies inside the auxiliary circle{see figure}Hence,radius of auxiliary circle is a = 3 units.By using distance formula, it is seen that the pt P lies inside the auxiliary circle. By substituting x=1 in eq1 we get y as  32/3 which is roughly less than 2.So,the pt P ( 1,2 ) lies outside the ellipse. Similarly we can do for pt Q also if necessary.
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Moderation Team
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