A set of points P(x,y)P(x, y)P(x,y) is defined by the parametric equations
x=t+23t−1,y=103t−1,t≠13 x = \frac{t + 2}{3t - 1}, \quad y = \frac{10}{3t - 1}, \quad t \neq \frac{1}{3} x=3t−1t+2,y=3t−110,t=31Show that all points P(x,y)P(x, y)P(x,y) lie on a straight line.
Hence or otherwise, find the x x\,x coordinate of the point of intersection of this line and the line with equation y=2x+11y = 2x + 11y=2x+11.
Practise AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane with exam-style questions for A Level Maths. 110 questions covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
