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If the distance between the foci of an ellipse is 8 and length of latus rectum is18/5, then the eccentricity of ellipse is: |
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Answer» `2/5` `rArr b^2=a^2-(ae)^2 rArr a^2=b^2+16` Length of L.R. `(2b^2)/a = 18/5 rArr b^2=9/5A` `rArr a^2=99/5 + 16 rArr 5a^2-99-80=0` `5a^2-25a+16a-80=0` `5a(a-5)+16(a-5)=0` (a-5)(5a+16)=0 `a=5 rArr e=4/5` |
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