Question

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

• A. $25x^2-144y^2=900$
• B. $144x^2-25y^2=900$
• C. $144x^2+25y^2=900$
• D. $25x^2+144y^2=900$

Answer 1

Answer: (A)

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