A hyperbola is centered at the origin, opens left and right, has vertices at $(\pm 4,0)$, and its fundamental rectangle reaches $y=\pm 3$. What is its equation?

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

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

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

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