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find an equation for the set of points in an xy-plane such that the sum of the distances from f and f' is k

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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.

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