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If the distance between the foci and the...

If the distance between the foci and the distance between the two directricies of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` are in the ratio 3:2, then `b : a` is (a)`1:sqrt(2)` (b) `sqrt(3):sqrt(2)` (c)`1:2` (d) `2:1`

A

`1:sqrt2`

B

`sqrt3:sqrt2`

C

`1:2`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that
`("Distance between foci")/("Distance between two directrices")=(3)/(2)`
`"or "(2ae)/(2*a//e)=(3)/(2)`
`"or "e^(2)=(3)/(3)`
`"or "1+(b^(2))/(a^(2))=(3)/(2)`
`"or "(b)/(a)=(1)/(sqrt2)`
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