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

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10-2. Parabola, Ellipse, Hyperbola

easy

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

A

$\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{12}} = 1$

B

$\frac{{{x^2}}}{{12}} - \frac{{{y^2}}}{4} = 1$

C

$\frac{{{y^2}}}{4} - \frac{{{x^2}}}{{12}} = 1$

D

$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{4} = 1$

Solution

(c) Foci $(0, \pm 4)$$ \equiv (0, \pm \,be)$

$⇒$ $be = 4$

Vertices $(0, \pm 2) \equiv (0, \pm b)$

$\Rightarrow b = 2 $

$\Rightarrow a = 2\sqrt 3 $

Hence equation is $\frac{{ – {x^2}}}{{{{(2\sqrt 3 )}^2}}} + \frac{{{y^2}}}{{{{(2)}^2}}} = 1$ or $\frac{{{y^2}}}{4} – \frac{{{x^2}}}{{12}} = 1$.

Standard 11

Mathematics

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