Question

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

• A. x212-y24=1
• B. x24-y212=1
• C. x28-y22=1
• D. x216-y29=1

Answer 1

The correct option is B x24-y212=1

In the standard hyperbola,

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

Given that eccentricity, $e=2$

Also distance between the foci is given by $2ae.$

Given,

$2ae=8\Rightarrow ae=4$

$\therefore a=\frac{4}{e}=2$

The lengths of transverse axis, conjugate axis and the eccentricity are related by

$b^2=a^2(e^2-1)$

i.e.,$b^2=4\times (4-1)=12$

$\therefore$ The required equation of hyperbola is,

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