Distance between foci is 8 and distance between directrices is 6 of hyperbola, then length of latusrectum is

Options

A. `4sqrt3`
B. `4/(sqrt3)`
C. `3/(sqrt4)`
D. None of these

Answer

B

Explanation

Given, `2ae=8and (2a)/(e)=6rArr2a=6e`

`therefore e^(2)=8/6rArre=2/sqrt3`
`rArr4/sqrt3a=8rArra=2sqrt3 and b^(2)=a^(2)(e^(2)-1)=12(4/3-1)=4`
`therefore length of latusrectum=(2b^(2))/(a)=(2x4)/(2sqrt(3))=4/sqrt3`