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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 2ae =8 rArr ae=4`
Also, `Z Z.=25`
`rArr (2a)/(e ) =25`
`rArr (2a)/(a)=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) xx 34`
`rArr b= sqrt(34)`
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