 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2002/paper-1/3/b/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

F (x, y) = x y^{3} - y x^{3} - 6 = 0

. Along the curve,

y^{'} = - \frac{F _{x}}{F _{y}} = - \frac{y ^{3} - 3 y x ^{2}}{3 x y ^{2} - x ^{3}} .

(1, 2)

F_{x} = 2

and

F_{y} = 11 \neq = 0

, so the slope is

- 2/11

y - 2 = - \frac{2}{11} (x - 1), equivalently 2 x + 11 y = 24.

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