Answer:
b) <em>Equation of the ellipse </em>
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Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>step(i)</em></u>:-
<em>Given the direct rices of the ellipse y = ±2</em>
<em>Given foci of the ellipse F( 0 ,± c) = ( 0,±1)</em>
<em>The the direct rices of the ellipse </em>
y = ± ![\frac{a}{e}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Be%7D)
![\frac{a}{e} = 2](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Be%7D%20%3D%202)
a = 2 e ...(i)
Given focus ( 0 , c) = ( 0, a e) = ( 0,1)
a e = 1 ...(ii)
From (i) and (ii)
2 e (e) = 1
2 e² = 1
![e^{2} = \frac{1}{2}](https://tex.z-dn.net/?f=e%5E%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
![e = \frac{1}{\sqrt{2} }](https://tex.z-dn.net/?f=e%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D)
<u><em>Step(ii):</em></u>-
Now a = 2 e = 2 (
)
a = √2
<em>Now we know that The relation between the focus and minor and major axes</em>
<em> formula C² = a² - b²</em>
<em> b² = a ² - C²</em>
<em> b² = 2 - 1 = 1</em>
<u><em>Step(iii)</em></u><em>:-</em>
<em>Equation of the ellipse</em>
<em> </em>
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<em> </em>
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<em> </em>
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<u><em>Conclusion:</em></u><em>-</em>
<em>Equation of the ellipse </em>
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<em> </em>