An ellipse graphed at the origin has x-intercepts at ($\pm 6$, $0$) and y-intercepts at ($0$, $\pm 2$). Which equation matches the graph?

$4x^2+36y^2=144$

$\frac{x^2}{4}+\frac{y^2}{36}=1$

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

$\frac{x^2}{36}+\frac{y^2}{4}=1$