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

The movement of a precision robotic arm across a flat surface is defined by the parametric relationship

\cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4}

where $x$ is the horizontal position in millimetres and $y$ is the control angle in radians.

Find $dxdy\frac{dx}{dy}$ in terms of $y$ .

[2]

Hence show that

\frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}}

where $k$ is a constant to be found.

[3]

A specific calibration point $P (a, b)$ lies on the path of the arm. Given that

find the exact values of $a$ and $b$ .

[4]

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