Find the equation for the ellipse that satisf | vedclass

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Question

(A) The ends of the major axis are $(0, \pm \sqrt{5})$,which implies the major axis lies along the $y$-axis.The ends of the minor axis are $(\pm 1, 0)

Vedclass · Accepted Answer

$x^2 + \frac{y^2}{5} = 1$

Vedclass · Answer

(A) The ends of the major axis are $(0, \pm \sqrt{5})$,which implies the major axis lies along the $y$-axis.The ends of the minor axis are $(\pm 1, 0)$,which implies the minor axis lies along the $x$-axis.The standard form of the equation for an ellipse with the major axis along the $y$-axis is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$,where $a$ is the semi-major axis and $b$ is the semi-minor axis.From the given coordinates,$a = \sqrt{5}$ and $b = 1$.Substituting these values into the standard equation:$\frac{x^2}{1^2} + \frac{y^2}{(\sqrt{5})^2} = 1$This simplifies to:$x^2 + \frac{y^2}{5} = 1$

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0, \pm \sqrt{5})$,ends of minor axis $(\pm 1, 0)$.

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