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:The centre is $(1,0)$, with horizontal semiaxis $\sqrt{3}$ and vertical semiaxis $\sqrt{3/2}$. Its four axis vertices are $(1\pm \sqrt{3},0)$ and $(1,\pm \sqrt{3/2})$; the ellipse meets the vertical coordinate axis at $(0,\pm 1)$.