Aspire Faculty ID #16662 · Topic: CUET 2023 · Just now
CUET 2023

Let $E$ be the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ and $C$ be the circle $x^2+y^2=9$. Let $P(1,2)$ and $Q(2,1)$ respectively. Then

Solution

For $P(1,2)$: Circle: $1^2+2^2=5<9$ ⇒ inside $C$ Ellipse: $\dfrac{1}{9}+\dfrac{4}{4}= \dfrac{1}{9}+1=\dfrac{10}{9}>1$ ⇒ outside $E$ So, $P$ lies inside $C$ but outside $E$.
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