2. Find the equation of the ellipse centered at the origin, with foci on the y-axis, eccentricity equal to 0.8, and focal distance of 4.
2. Let the equation of the ellipse be $\frac{\mathrm{x}^{2}}{\mathrm{~b}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{a}^{2}}=1$. From the problem, we have: $2 \mathrm{c}=4, \mathrm{c}=2$.
$$
\left\{\begin{array}{l}
a^{2}-b^{2}=4, \\
\frac{2}{a}=0.8 .
\end{array}\right.
$$

Solving these, we get $\mathrm{a}=\frac{5}{2}, \mathrm{~b}=\frac{3}{2}$.
The required equation of the ellipse is $\frac{4 x^{2}}{9}+\frac{4 y^{2}}{25}=1$.