 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/15/a/solution

D (x, y) = x^{2} + y^{2}

D^{2} = a^{2} cosh^{2} t + b^{2} sinh^{2} t = a^{2} + (a^{2} + b^{2}) sinh^{2} t .

This is at least

a^{2}

, with equality exactly when

t = 0

. Therefore

(x_{m}, y_{m}) = (a, 0), D_{m i n} = a .

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