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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. Then
  1. Q lies inside C but outside E
  2. Q lies outside both C and E
  3. P lies inside both C and E
  4. P lies inside C but outside E


Solution

The correct option is D P lies inside C but outside E
For circle x2+y2=9 
point P is (1,2) and Q is (2,1)
Since 12+229<0 and 22+129<0
Both P and Q lie inside C.

For x29+y24=1
Also 129+2241>0 and 229+1241<0
P lies outside E and Q lies inside E.
Thus P lies inside C but outside E. 

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