 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/9/a/solution

Subtracting the two circle equations cancels the common terms and gives

- 4 x = 0

. With

x = 0

, either circle equation gives

(y - 1)^{2} = 0

. Thus the unique common point is

(x, y) = (0, 1) .

The two circles touch externally there.

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