Question

The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

conjugate axis is 5 and distance between foci=13 $\Rightarrow 2b=5$ and 2ae=13.
Now, also we know for hyperbola
$b^2=a^2(e^2-1)\Rightarrow \frac{25}{4}=\frac{(13{)}^2}{4e^2}(e^2-1)$
$\Rightarrow \frac{25}{4}=\frac{169}{4}-\frac{169}{4e^2}or{e}^2=\frac{169}{144}\Rightarrow e=\frac{13}{12}$
or a=6, b=$\frac{5}{2}$ or hyperbola is $\frac{x^2}{36}-\frac{y^2}{\frac{25}{4}}=1$
$\Rightarrow 25x^2-144y^2=900$