Equation to hyperbola having its eccentricity 2 and distance between its foci is 8

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10-2. Parabola, Ellipse, Hyperbola

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The equation to the hyperbola having its eccentricity $2$ and the distance between its foci is $8$

A

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

B

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

C

$\frac{{{x^2}}}{8} - \frac{{{y^2}}}{2} = 1$

D

$\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1$

Solution

(b) Distance between foci = $8$

$2ae = 8$ also $e = 2$; $2a = 4$

==> $a = 2$

==> ${a^2} = 4$;

${b^2} = 4(4 – 1) = 12$

Equation of hyperbola is $\frac{{{x^2}}}{4} – \frac{{{y^2}}}{{12}} = 1$.

Standard 11

Mathematics

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