Question

Find the equation of the hyperbola whose foci are $(\pm 5,0)$ and the length of transverse axis is $8$.

Answer 1

Since length of transverse axis is 8 and the foci are located on the x-axis, the transverse axis is also on the x-axis. We have $2a=8\Rightarrow a=4$ and $ae=5\Rightarrow e=1.25$

$e^2=1+\frac{b^2}{a^2}=\frac{25}{16}\Rightarrow b=3$

Thus the equation of the hyperbola is

$\frac{x^2}{16}-\frac{y^2}{9}=1$