 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/11/c/solution

Read the squared semiaxis lengths from the denominators in the standard equation obtained in (b). With the positive choice of

C

there,

a = \frac{A}{C ^{2}}, b = \frac{1}{C} .

Since

C^{2} = A^{2} - B^{2} < A^{2}

, the horizontal semiaxis

a

is the larger. Thus these are the semi-major and semi-minor axes, respectively.

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