 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/8/solution

Divide by four and use completing the square:

x^{2} - 2 x + y^{2} + y = \frac{11}{4}, (x - 1)^{2} + (y + \frac{1}{2})^{2} = 4.

This is the standard equation of a circle, so

centre = (1, - 1/2), radius = 2.

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