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.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.