Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

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,

$2ae=8$

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.,$b^2=4.(4-1)$

=12.

$\therefore$ The required equation of hyperbola is,

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