 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/2/solution

Complete the squares in the two coordinates:

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

This standard equation of an ellipse is symmetric about

x = 2

and

y = 1

. Its centre is therefore

(2, 1) .

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