Question

Find the equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$.

• A. $25x^2-144y^2=900$
• B. $144x^2-25y^2=900$
• C. $3x^2-16y^2=80$
• D. $16x^2-3y^2=80$

Answer 1

The correct option is A $25x^2-144y^2=900$

Equation of hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

We have, $2b=5,2ae=13$

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

$b^2=a^2{e}^2-a^2$

$\frac{25}{4}=\frac{169}{4}-a^2$

$a^2=\frac{144}{4}$

$a=6$

Thus, the required equation of hyperbola is :

$\frac{x^2}{36}-\frac{y^2}{25/4}=1$

$25x^2-144y^2=900$