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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/6/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2008 / Paper 1 / 6 / Solution by

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

The point on the parabola is

(1, 2)

. Implicit differentiation gives

2 y d y / d x = 4

, so the tangent line has slope one there. Its perpendicular normal line to a plane curve therefore has slope

- 1

. The required line is

y - 2 = - (x - 1), or y = 3 - x .

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