 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/5/b/solution

Put the equation into standard ellipse form:

\frac{( x - 1 ) ^{2}}{3} + \frac{y ^{2}}{3/2} = 1.

The centre is

(1, 0)

, with horizontal semiaxis

3

and vertical semiaxis

3/2

. Its four axis vertices are

(1 \pm 3, 0)

and

(1, \pm 3/2)

; the ellipse meets the vertical coordinate axis at

(0, \pm 1)

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