The eccentricity of the conjugate hyperbola of the hyperbola `x^2-3y^2=1` is (a) 2 (b) `2sqrt(3)` (c) 4 (d) `4/5`

Options

A. `2`
B. `(2)/(sqrt(3))`
C. `4`
D. `(4)/(3)`

Answer

A

Explanation

Let `e` be the eccentricity of `x^(2)-3y^(2)=1`. Then, `e^(2)=1+(1)/(3)=(4)/(3)`
Let `e_(1)` be the eccentricity of the conjugate hyperbola. Then,
`(1)/(e^(2))+(1)/(e_(1)^(2))=1implies(1)/(e_(1)^(2))=1-(3)/(4)=(1)/(4)impliese_(1)=2`