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  • The equation of the ellipse whose latus rectum is 8 and whose eccentricity is <img alt="\frac{1}{\sqrt{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D"

The equation of the ellipse whose latus rectum is 8 and whose eccentricity is \frac{1}{\sqrt{2}} , referred to the principal axes of coordinates, is
 

Option: 1

\mathrm {\frac{x^2}{18}+\frac{y^2}{32}=1}


Option: 2

\mathrm {\frac{x^2}{8}+\frac{y^2}{9}=1}


Option: 3

\mathrm {\frac{x^2}{64}+\frac{y^2}{32}=1}


Option: 4

\mathrm {\frac{x^2}{16}+\frac{y^2}{24}=1}


Answers (1)

best_answer

\mathrm {\frac{2 b^2}{a}=8, e=\frac{1}{\sqrt{2}} \Rightarrow a^2=64, b^2=32}
Hence, required equation of ellipse is  \mathrm {\frac{x^2}{64}+\frac{y^2}{32}=1.}

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