InterviewSolution
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InterviewSolution
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If the latus rectum of an ellipse is equal to the half of minor axis, then find its eccentricity. |
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Answer» Consider the equation of the ellipse is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` `therefore`Length of major axis=2a Length of minor axis=2b and length of latusrectum=`(2b^(2))/a` Given that, `(2b^(2))/a=(2b)/2` `rArr` a=2b`rArr`b=a/2 We know that, `b^(2)=a^(2)(1-e^(2))` `rArr (a/2)^(2)=a^(2)(1-e^(2))` `rArr(a^(2))/4=a^(2)(1-e^(2))` `rArr1-e^(2)=1/4` `rArre^(2)=1-1/4` `therefore e=sqrt(3/4)=sqrt(3/2)` |
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