Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0,\, \pm \sqrt{5})$ ends of minor axis $(±1,\,0)$
Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0,\, \pm \sqrt{5})$ ends of minor axis $(±1,\,0)$
Ends of major axis $(0, \,\pm \sqrt{5}),$ ends of minor axis $(±1,\,0)$
Here, the major axis is along the $y-$ axis.
Therefore, the equation of the ellipse will be of the form $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1,$ where a is the semimajor axis.
Accordingly, $a =\sqrt{5}$ and $b=1$
Thus, the equation of the ellipse is $\frac{x^{2}}{1^{2}}+\frac{y^{2}}{(\sqrt{5})^{2}}=1$ or $\frac{x^{2}}{1}+\frac{y^{2}}{5}=1$
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