Equation for ellipse that satisfies given conditions: Ends of major axis (0,, pm √{5}) ends of min

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10-2. Parabola, Ellipse, Hyperbola

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

Option A

Option B

Option C

Option D

Solution

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

Standard 11

Mathematics

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