Answer
The set of all points above the ellipse centered at $C\left(\frac{x_{2}+x_{1}}{2}, \frac{y_{2}+y_{1}}{2}\right)$ with focus at $\left(x_{2}, y_{2}\right)$ , $\left(x_{1}, y_{1}\right)$
Work Step by Step
Let $\vec{r}_{2}=\left\langle x_{2}, y_{2}\right\rangle, \quad \vec{r}_{1}=\left\langle x_{1}, y_{1}\right\rangle \quad$ and $\vec{r}=\langle x, y\rangle .$ If
\[
K=\left\|-\vec{r}_{1}+\vec{r}\right\|+\left\|-\vec{r}_{2}+\vec{r}\right\|
\]
The equation corresponds to the set of all points in 2d-space that are over an ellipse.
Let us consider that the initial point of all vectors $\vec{r}$ is at the origin, so:
$\left\|-\vec{r}_{1}+\vec{r}\right\| \rightarrow$ is the distance between the terminal points $\left\|-\vec{r}_{2}+\vec{r}\right\| \longrightarrow$ is the distance between the terminal points
Since $ \vec {r} _ {1} $ and $ \vec {r} _ {2} $ are fixed, the equation corresponds to the set of all points a distance 2 above the ellipse that focus on the endpoints. This ellipse is centered at the midpoint of the focus:
\[
C\left(\frac{x_{2}+x_{1}}{2}, \frac{y_{2}+y_{1}}{2}\right)
\]
