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  • The equation of an ellipse in standard form, whose foci are and eccentricity is <img alt="\frac

The equation of an ellipse in standard form, whose foci are ( \pm 2,0) and eccentricity is \frac{1}{2}, is
 

Option: 1

\mathrm{\frac{x^2}{16}+\frac{y^2}{12}=1}
 


Option: 2

\mathrm{\frac{x^2}{12}+\frac{y^2}{16}=1}
 


Option: 3

\mathrm{\frac{x^2}{16}+\frac{y^2}{4}=1}
 


Option: 4

\mathrm{\frac{x^2}{9}+\frac{y^2}{16}=1}


Answers (1)

best_answer

Let the ellipse be \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}=1.}

As \mathrm{\quad O S \equiv a e=2\: and \: e=\frac{1}{2}}

\mathrm{\Rightarrow \quad a=4}

Also \mathrm{b^2=a^2\left(1-e^2\right)}

            \mathrm{ =16\left(1-\frac{1}{4}\right)=12 }

\mathrm{ \therefore \quad \text{the ellipse is }\frac{x^2}{16}+\frac{y^2}{12}=1 }

Hence option 1 is correct.

    

           


 

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