Let E be the ellipse frac{x^2}{9} + frac{y^2} | vedclass

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(D) For the ellipse $E: \frac{x^2}{9} + \frac{y^2}{4} - 1 = 0$,let $f(x, y) = \frac{x^2}{9} + \frac{y^2}{4} - 1$.For the circle $C: x^2 + y^2 - 9 = 0$

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$P$ lies inside $C$ but outside $E$.

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(D) For the ellipse $E: \frac{x^2}{9} + \frac{y^2}{4} - 1 = 0$,let $f(x, y) = \frac{x^2}{9} + \frac{y^2}{4} - 1$.For the circle $C: x^2 + y^2 - 9 = 0$,let $g(x, y) = x^2 + y^2 - 9$.For point $P(1, 2)$:$f(1, 2) = \frac{1}{9} + \frac{4}{4} - 1 = \frac{1}{9} > 0$,so $P$ is outside $E$.$g(1, 2) = 1^2 + 2^2 - 9 = 1 + 4 - 9 = -4 Thus,$P$ lies inside $C$ but outside $E$.For point $Q(2, 1)$:$f(2, 1) = \frac{4}{9} + \frac{1}{4} - 1 = \frac{16 + 9 - 36}{36} = -\frac{11}{36} $g(2, 1) = 2^2 + 1^2 - 9 = 4 + 1 - 9 = -4 Thus,$Q$ lies inside both $C$ and $E$.

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:

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