 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-1/1b/a/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

By the focal definition of an ellipse, the solution set is the ellipse with foci

a

and

b

. Its centre is

(a + b) /2

, its major axis lies along the line through the foci, and its semiaxes are

\frac{c}{2}, \frac{1}{2} c^{2} - ∣ a - b ∣^{2} .

The sketch is consequently a nondegenerate ellipse symmetric about both the focal line and its perpendicular bisector.

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