If $(0, \pm 4)$ and $(0, \pm 2)$ be the foci and vertices of a hyperbola, then its equation is

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Solution

The correct option is C

Foci $(0, \pm 4) \equiv (0, \pm b e) \Rightarrow b e = 4$
Vertices $(0, \pm 2) \equiv (0, \pm b) \Rightarrow b = 2 \Rightarrow a = 2 \sqrt{3}$
Hence equation is $\frac{- x^{2}}{(2 \sqrt{3})^{2}} + \frac{y^{2}}{(2)^{2}} = 1 o r \frac{y^{2}}{4} - \frac{x^{2}}{12} = 1$ .

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