On the x-y plane, the eccentricity of an ellipse is fixed (in size and position) by

If both the foci are fixed, then the ellipse is fixed, that is, both the directrices can be decided (eccentricity is given). Similar is the case for option (c). Thus, (a) and (c) are the correct choices. In the remaining cases, the size of the ellipse is fixed, but its position is not fixed.