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Filnd the distance between the directric...

Filnd the distance between the directrices the ellipse `(x^2)/(36)+(y^2)/(20)=1.`

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The equation of ellipse is `(x^(2))/36+(y^(2))/20=1`
On comparing this equation with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` we get
`a=6,b=2sqrt5`
we know that, `b^(2)=a^(2)(1-e^(2))` ltbr. `rArr 20=36(1-e^(2))`
`rArr 20/36=1-e^(2)`
`therefore e=sqrt(1-20/36)=sqrt(16/36)`
`E=4/6=2/3`
Now, directrices=`(+a/e,-1/e)`
`therefore a/e=(6/2)/3=(6xx3)/2=9`
and `-a/e=-9`
`therefore` Distance between the directrices=`abs(9-(-9))=18`
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