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

Options

A. `(5)/(sqrt(17))`
B. `(3)/(sqrt(17))`
C. `(4)/(sqrt(17))`
D. `(6)/(sqrt(17))`

Answer

A

Explanation

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)`