3.3 Coordinate geometry in the (x, y) plane (A-level only)

The path of a robotic arm in a two-dimensional manufacturing grid $(X, Y)$ is defined by the parametric equations

\frac{2p - 5}{1 - 4p}, \quad Y = \frac{12}{1 - 4p}, \quad p \neq \frac{1}{4}

where $p\,$ is a control parameter.

Show that the robotic arm moves along a straight line.

[4]

The arm's path intersects a safety perimeter defined by the line $Y = 3 X + 10$ . Determine the $X$ -coordinate of this point of intersection.

[3]

3.3 Coordinate geometry in the (x, y) plane (A-level only) Questions

The path of a robotic arm in a two-dimensional manufacturing grid $(X, Y)$ is defined by the parametric equations

\frac{2p - 5}{1 - 4p}, \quad Y = \frac{12}{1 - 4p}, \quad p \neq \frac{1}{4}

where $p\,$ is a control parameter.

Show that the robotic arm moves along a straight line.

[4]

The arm's path intersects a safety perimeter defined by the line $Y = 3 X + 10$ . Determine the $X$ -coordinate of this point of intersection.

[3]