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10-2. Parabola, Ellipse, Hyperbola
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Let $'E'$ be the ellipse $\frac{{{x^2}}}{9}$$+$$\frac{{{y^2}}}{4}$ $= 1$ $\& $ $'C' $ be the circle $x^2 + y^2 = 9.$ Let $P$ $\&$ $Q$ be the points $(1 , 2) $ and $(2, 1)$ respectively. Then :
A
$Q$ lies inside $C$ but outside $E$
B
$Q$ lies outside both $C$ $\&$ $ E$
C
$P$ lies inside both $C$ $ \&$ $E$
D
$P$ lies inside $C$ but outside $E.$
Solution
$E :\left( x ^{2} / 9\right)+\left( y ^{2} / 4\right)=1$ and $C : x ^{2}+ y ^{2}=9$
given: $P (1,2)$
Now $1^{2}+2^{2}-9<0 \Rightarrow P$ is inside circle $C$.
also $(1 / 9)+(4 / 4)>1 \Rightarrow P$ is outside ellipse $E$
For $Q(2,1)$
Now $2^{2}+1^{2}-9<0 \Rightarrow Q$ is inside circle $C$.
also $(4 / 9)+(1 / 4)<1 \Rightarrow Q$ is inside ellipse $E$
$\Rightarrow P$ lies inside $C$ but outside $E$
Standard 11
Mathematics
