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1.5.16 Gradient of a parametric curve (A-level only)

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Question 24

The trajectory of a specialized particle in a particle accelerator is modeled by the curve C C\,C with equation

x=ye−4y,y∈R x = y e^{-4y}, \quad y \in \mathbb{R} x=ye−4y,y∈R
a.

Show that

dydx=yx(1−4y) \frac{\mathrm{d} y}{\mathrm{d} x} = \frac{y}{x(1 - 4y)} dxdy​=x(1−4y)y​
[3]
b.

Given that a vertical detector strip at x=kx = kx=k, where k k\,k is a constant, detects the particle at exactly two distinct locations on the curve CCC,

find the range of possible values for kkk.

[4]

1.5.16 Gradient of a parametric curve (A-level only) Questions

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