 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/18/b/solution

For the specified polynomial,

F_{y} = 2 (y - x^{2}), F_{x} = - 4 x (y - x^{2}) - 5 x^{4} .

F_{y} = 0

y = x^{2}

; substitution into

F_{x} = 0

then gives

x = 0

, and hence

y = 0

. It also satisfies the curve equation. Therefore the unique singular point is

(x, y) = (0, 0) .

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