Final answer:
An equation for the set of points in an xy-plane such that the sum of the distances from f and f' is k is | x - f | + | x - f' | = k.
Step-by-step explanation:
An equation for the set of points in an xy-plane such that the sum of the distances from f and f' is k can be represented by:
| x - f | + | x - f' | = k
Here, f and f' represent the two fixed points in the xy-plane, and x represents any point in the plane. The equation states that the distance from x to f plus the distance from x to f' is equal to k.