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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/11/b/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 11 / b / ii / Solution by

Codex  0 2026-10-18

The triangle inequality bounds the distance sum below by the separation of the two foci, which is two. Equality holds exactly for points on the closed segment joining them. Hence the locus is

x = 0, 0 \leq y \leq 2, equivalently z = i y (0 \leq y \leq 2) .

(1)

Both endpoints are included. It is the segment on the positive imaginary axis shown in the right-hand panel above.

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