 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/2/solution

d y / d x = 2 + 2 x

4

(1, 3)

. A normal line to a plane curve has the negative reciprocal slope, since its direction is orthogonal to a tangent vector. Hence

y - 3 = - \frac{1}{4} (x - 1), x + 4 y = 13.

The point

(1, 3)

satisfies the equation, and the product of the two slopes is

- 1

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