Answer
See explanations.
Work Step by Step
Step 1. Decide major and minor axes: as $k\gt0$, we have $4+k\gt k$ so that the major axis is vertical.
Step 2. Compare the equation with a standard ellipse $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$, we have
$b^2=k$ and $a^2=4+k$
Step 3. Use the relationship $c^2=a^2-b^2$ we get $c^2=4+k-k=4$ thus $c=2$ which is independent of $k$
Step 4. Conclusion: all the ellipses represented by this equation have the same foci $(0, \pm2)$, no matter what the value of k.
