The Foci of an Ellipse

The eccentricity of an ellipse is a value $e \in [0, 1)$. There are many ways to define eccentricity; one way to describe it is that the lower the eccentricity, the more "circular" an ellipse is.

One way to calculate the eccentricity of an ellipse is $e = \frac{f}{a}$, where $f$ is the distance from the center to each focus and $a$ is the length of the semi-major axis. (This is the same $a$ found in the equation for an ellipse.)

That being said, if $E$ is an ellipse with center $(3,4)$ and eccentricity $\frac{\sqrt{2}}{2}$, and the farthest distance between two points on $E$ is $4$, which of these could be the coordinates of the foci?