10. A certain ellipse is centered at the origin, with an eccentricity of $\frac{1}{2}$, and the distance from a focus to the corresponding directrix is 3. The equation of the ellipse is $\qquad$.
10. $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ or $\frac{x^{2}}{3}+\frac{y^{2}}{4}=1$

From the problem, $e=\frac{c}{a}=\frac{1}{2} \cdot \frac{a^{2}}{c}-c=3$,
solving simultaneously gives $a=2, c=1 \Rightarrow b=\sqrt{3}$.
Therefore, the equations are $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ or $\frac{x^{2}}{3}+\frac{y^{2}}{4}=1$.