An ellipse,with foci at (0, 2) and (0, -2) an | vedclass

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(D) The foci are at $(0, \pm c)$ where $c = 2$. Since the foci lie on the $y$-axis,the ellipse is vertical.The length of the minor axis is $2a = 4$,so

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$(\sqrt{2}, 2)$

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(D) The foci are at $(0, \pm c)$ where $c = 2$. Since the foci lie on the $y$-axis,the ellipse is vertical.The length of the minor axis is $2a = 4$,so $a = 2$.For an ellipse,$c^2 = b^2 - a^2$,where $b$ is the semi-major axis.$2^2 = b^2 - 2^2$ $\Rightarrow 4 = b^2 - 4$ $\Rightarrow b^2 = 8$.The equation of the ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,which is $\frac{x^2}{4} + \frac{y^2}{8} = 1$.Testing option $(D)$: $\frac{(\sqrt{2})^2}{4} + \frac{2^2}{8} = \frac{2}{4} + \frac{4}{8} = \frac{1}{2} + \frac{1}{2} = 1$.Thus,the point $(\sqrt{2}, 2)$ lies on the ellipse.

An ellipse,with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$,passes through which of the following points?

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