Answer
$\displaystyle \frac{x^{2}}{4}-\frac{\mathrm{y}^{2}}{9}=1,\ \ \ $ (hyperbola)
Foci: $\qquad (\pm\sqrt{13}, 0)$
Asymptotes:$\displaystyle \quad y=\pm\frac{3}{2}x$
Work Step by Step
Hyperbola, horizontal axis.
Foci on the x-axis: $\quad \displaystyle \frac{x^{2}}{a^{2}}-\frac{\mathrm{y}^{2}}{b^{2}}=1$
The equation of this form is $\quad \displaystyle \frac{x^{2}}{4}-\frac{\mathrm{y}^{2}}{9}=1$
We read: $a=2,\quad b=3$
Foci: $(\pm c, 0),\qquad c=\sqrt{a^{2}+b^{2}}$
$c=\sqrt{4+13}=\sqrt{13}$
So the foci are at $(\pm\sqrt{13}, 0)$
Asymptotes:$\displaystyle \quad y=\pm\frac{b}{a}x$
$y=\displaystyle \pm\frac{3}{2}x$