Design an elliptical garden with major axis length $20$ and minor axis length $12$, centered at the origin with horizontal major axis. Provide the standard-form equation and the distance from the center to each focus.

$\frac{x^2}{10}+\frac{y^2}{6}=1$

foci at ($\pm 4$, $0$)

$\frac{x^2}{100}+\frac{y^2}{36}=1$

foci at ($\pm 6$, $0$)

$\frac{x^2}{100}+\frac{y^2}{36}=1$

foci at ($\pm 8$, $0$)

$\frac{x^2}{36}+\frac{y^2}{100}=1$

foci at ($0$, $\pm 8$)