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//sqrt3`
C. 4
D. `4//5`

Explanation

To find the eccentricity of the conjugate hyperbola of the hyperbola given by the equation \( x^2 - 3y^2 = 1 \), we will follow these steps:

### Step 1: Identify the standard form of the hyperbola
The given hyperbola can be rewritten in the standard form:
\[ \frac{x^2}{1} - \frac{y^2}{\frac{1}{3}} = 1 \]
Here, we can identify \( a^2 = 1 \) and \( b^2 = \frac{1}{3} \).
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