Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1542 Upvotes
Verified Answer
The correct answer is:
$P$ lies inside $C$ but outside $E$
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 $E$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.