Conic Sections Question 306
Question: Let E be the ellipse $ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $ and C be the circle $ x^{2}+y^{2}=9 $ . Let P and Q be the points (1, 2) and (2, 1) respectively. Then
[IIT 1994]
Options:
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 C but outside E
Show Answer
Answer:
Correct Answer: D
Solution:
The given ellipse is $ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $ . The value of the expression $ \frac{x^{2}}{9}+\frac{y^{2}}{4}-1 $ is positive for $ x=1,y=2 $ and negative for $ x=2,y=1 $ . Therefore P lies outside E and Q lies inside E. The value of the expression $ x^{2}+y^{2}-9 $ is negative for both the points P and Q. Therefore P and Q both lie inside C.
Hence P lies inside C but outside E.
BETA
