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 `1:sqrt(2)` (b) `sqrt(3):sqrt(2)` `1:2` (d) `2:1`

Options

A. `1:sqrt2`
B. `sqrt3:sqrt2`
C. `1:2`
D. `2:1`

Answer

A

Explanation

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)`