Question

$C:x^2+y^2=9$, $E:\frac{x^2}{9}+\frac{y^2}{4}=1$, $L:y=2x$

Let $L$ intersect $x=1$ at point $R$. Then which of the following is correct :

• A. $R$ lies inside both $C$ and $E$
• B. $R$ lies outside both $C$ and $E$
• C. $R$ lies on both $C$ and $E$
• D. $R$ lies inside $C$ but outside $E$

Answer 1

The correct option is D $R$ lies inside $C$ but outside $E$

$y=2x$, intersects $x=1$ at $(1,2)$
Coordinate of $R$ are $(1,2)$
$C(1,2)=1+22-9<0$ Since $C(1,2)$ is $<0,R$ lies inside $C$
$E(1,2)=\frac{1}{9}+1-1>0$ Since $E(1,2)$ is $>0,R$ lies outside $E$.