B4. A circle with radius $r=4$ has its center at one of the vertices of the ellipse $b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2}$ and passes through both foci and the other vertex. Write the equation of the ellipse $(a>b)$!

## Solutions to problems

## First year

I. PART

| 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- |
| $\mathrm{D}$ | $\mathrm{D}$ | $\mathrm{E}$ | $\mathrm{E}$ | $\mathrm{A}$ | $\mathrm{B}$ |