If the distance between the foci and the distance between the directrices of the hyperbola `x^(2)/(a_2 )-y^(2)/b_2 =1` are in the ratio 3:2

Options

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

Answer

B

Explanation

Equation of hyperbola is `x^(2)/a^(2)-y^(2)/b^(2)=1` distance between foci of hyperbola =2ae and its distance between directrices =2a/e according to the question, `(2ae)/(2a/e)=3/2 rArre^(2)=3/2 `
` using" b^(2)=a^(2)(e^(2)-1)`
`rArrb^(2)/a^(2)=3/2-1`
`therefore a/b =sqrt2/1`