= 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 $\sqrt3$ and vertical semiaxis $\sqrt{3/2}$. Its four axis vertices are $(1\pm\sqrt3,0)$ and $(1,\pm\sqrt{3/2})$; the <ellipse> meets the vertical coordinate axis at $(0,\pm1)$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1-ellipse.png]
{title=The displaced ellipse with its centre, semiaxes and coordinate-axis intersections}
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