Which of the following combinations will NOT define an ellipse?

An ellipse can be defined by its semi-major axis (a) and one of the following: eccentricity (e), focal distance (f), or the reciprocal of the focal distance (1/f). The semi-major axis represents the longest radius of the ellipse, and the other parameters provide additional geometric information that helps to specify the shape and size of the ellipse.

The pair consisting of the semi-major axis (a) and eccentricity (e) is sufficient for defining an ellipse. The eccentricity provides a measure of how much the conic section deviates from being circular, allowing for a unique definition of an ellipse based on these two parameters.

In contrast, the combination involving semi-major axis (a) and focal distance (f) would also be able to define an ellipse. Furthermore, the semi-major axis (a) along with its inverse focal length (1/f) can describe an ellipse, as both of these parameters are related to the shape of the ellipse.

The combination of the eccentricity (e) and focal distance (f) can also define an ellipse, since both describe characteristics of the ellipse's geometry.

The important takeaway is that the combination of the semi-major axis (a) and eccentricity (e) uniquely defines an ellipse