 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/3/solution

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

The locus is therefore a circle with centre $(1, 0)$ and radius $2$ . It meets the horizontal axis at

(- 1, 0)

and

(3, 0)

and the vertical axis at

(0, \pm 3)

; its highest and lowest points are

(1, \pm 2)

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