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  • If the distance between the foci of an ellipse is 5 and the distance between its directrices is 12, then the length of its latus rectum is:Option: 1</s

If the distance between the foci of an ellipse is 5 and the distance between its directrices is 12, then the length of its latus rectum is:

Option: 1

\begin{aligned} & \frac{119}{25} \\ \end{aligned}


Option: 2

\frac{109}{25} \\


Option: 3

\frac{109}{20} \\


Option: 4

\frac{109}{15}


Answers (1)

best_answer

\begin{aligned} =e^2=1-\frac{b^2}{a^2} \\ \Rightarrow \frac{1}{2}=1-\frac{b^2}{18} \\ \Rightarrow \frac{1}{2}=\frac{b^2}{18} \end{aligned}

\Rightarrow b^2=9

Length of latus rectum  =\frac{2 b^2}{a}

                                        =\frac{119}{25}

Posted by

Divya Prakash Singh

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