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Q.

The eccentricity of the hyperbola with latus rectum 12 and semi-conjugate axis 2 $\sqrt{3}$ , is

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a

2

b

3

c

$\sqrt{3} / 2$

d

2 $\sqrt{3}$

answer is A.

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Detailed Solution

$2 \cdot \frac{b^{2}}{a} = 12$ and $b = 2 \sqrt{3}$

$\begin{array}{l} ∴ a = 2 a n d e^{2} = 1 + \frac{b^{2}}{a^{2}} = 1 + 3 = 4 \\ \Rightarrow e = 2 \end{array}$

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The eccentricity of the hyperbola with latus rectum 12 and semi-conjugate axis 23, is