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In an ellipse the distance between the f...

In an ellipse the distance between the foci is 8 and the distance between the directrices is 25, then the ratio of the length of major and minor axis is

A

`(5)/(sqrt(17))`

B

`(3)/(sqrt(17))`

C

`(4)/(sqrt(17))`

D

`(6)/(sqrt(17))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `F_(1)F_(2)=8 rArr 2a e=8 rArr ae = 4 `
Also, `Z Z'=25`
`rArr (2a)/(e )=25`
`rArr (2a)/((4)/(a))=25" " e=(4)/(a)`
`rArr 2a^(2)=25xx4=100 =(4)/(5sqrt(2))`

`rArr a^(2)=50`
`rArr a=5sqrt(2)`
`:.b^(2)=a^(2)(1-e^(2)) " Ratio"=(5sqrt(2))/(sqrt(34))`
`=50(1-(16)/(50)) " " =(5)/(sqrt(17))`
`=(50)/(50)xx34`
`rArr b=sqrt(34)`
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