 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/11/c/ii/solution

Adding

4 + 3 i

(4, 3)

in the complex plane. The ellipse of part (i) therefore keeps its semiaxes and axis directions, with new centre

(2, 2)

v = X + iY

, its equation is

\frac{( X - 2 ) ^{2}}{1 6 ^{2}} + \frac{( Y - 2 ) ^{2}}{8 ^{2}} = 1.

The third panel in the figure in part (b) shows the translated ellipse.

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