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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.