Equation of the hyperbola whose conjugate axis is of length 4 and the distance between foci is 12 is

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$\frac{x^{2}}{4} - \frac{y^{2}}{32} = 1$

$\frac{x^{2}}{32} - \frac{y^{2}}{4} = 1$

$\frac{x^{2}}{32} - \frac{y^{2}}{16} = 1$

$\frac{x^{2}}{16} - \frac{y^{2}}{32} = 1$

answer is B.

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Detailed Solution

$Let H \equiv \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
$given that 2 b = 4$
$\begin{array}{l} \Rightarrow b = 2 \\ 2 a e = 12 \Rightarrow a e = 6 \\ a^{2} + b^{2} = a^{2} e^{2} = 36 \Rightarrow a^{2} = 32 \end{array}$

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