Question

# Let E be the ellipse x29+y24=1 and C be the circle x2+y2=9. Let P and Q be the points (1,2) and (2,1) respectively. ThenQ lies inside C but outside EQ lies outside both C and EP lies inside both C and EP lies inside C but outside E

Solution

## The correct option is D P lies inside C but outside EFor circle x2+y2=9  point P is (1,2) and Q is (2,1) Since 12+22−9<0 and 22+12−9<0 ⇒ Both P and Q lie inside C. For x29+y24=1 Also 129+224−1>0 and 229+124−1<0 ⇒P lies outside E and Q lies inside E. Thus P lies inside C but outside E.

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