Answer
$\frac{x^2}{9}-\frac{y^2}{16}=1$
Work Step by Step
Foci: $(±c,0)=(±5,0)$
$c=5$
Major axis ishorizontal.
Length $=2a=6$
$a=3$
$c^2=a^2+b^2$
$b^2=c^2-a^2=5^2-3^2=25-9=16$
$b=4$
Hyperbola with horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{x^2}{3^2}-\frac{y^2}{4^2}=1$
$\frac{x^2}{9}-\frac{y^2}{16}=1$
