Which term best describes the set of all points in a plane for which the sum
of the distances to two fixed points equals a certain constant?

elipse

step-by-step explanation:

in mathematics, an  ellipse  is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. as such, it is a generalization of a circle, which is a special type of an  ellipse having both focal points at the same location.