InterviewSolution
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InterviewSolution
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If the eccentricity of an ellipse is `5/8`and the distance between its foci is `10 ,`then find the latusrectum ofthe ellipse. |
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Answer» Given that, eccentricity=`5/8i.e.,e=5/8` Let equation of the ellipse be `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` ltvbrgt since the foci of the ellipse is `)pmae,o)`. `therefore` Distance between foci =`sqrt((ae+ae)^(2))` `rArr 2sqrt(a^(2)e^(2))=10` [`because` distance between the foci=10] `rArr sqrt(a^(2)e^(2))=5` `rArr a^(2)e^(2)=25` `rArr a^(2)=(25xx64)/25` `thereforea=8` We know that, `rArr b^(2)=a^(2)(1-e^(2))` `rArr b^(2)=64(1-25/64)` `rArr b^(2)=64((64-25)/64)` `b^(2)=39` `therefore` Length of latusrectum of ellipse=`(2b^(2))/a=2(39/8)=39/4` |
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