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

A set of points $P (x, y)$ is defined by the parametric equations

\frac{t + 2}{3t - 1}, \quad y = \frac{10}{3t - 1}, \quad t \neq \frac{1}{3}

Show that all points $P (x, y)$ lie on a straight line.

[4]

Hence or otherwise, find the $x\,$ coordinate of the point of intersection of this line and the line with equation $y = 2 x + 11$ .

[3]

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

A set of points $P (x, y)$ is defined by the parametric equations

\frac{t + 2}{3t - 1}, \quad y = \frac{10}{3t - 1}, \quad t \neq \frac{1}{3}

Show that all points $P (x, y)$ lie on a straight line.

[4]

Hence or otherwise, find the $x\,$ coordinate of the point of intersection of this line and the line with equation $y = 2 x + 11$ .

[3]