 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/5/solution

Use completing the square in each coordinate:

(x - 3)^{2} - 9 + (y - 1)^{2} - 1 + 1 = 0, (x - 3)^{2} + (y - 1)^{2} = 9.

Comparing with the standard circle equation gives

centre (3, 1), radius 3.

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