A drone's horizontal distance d d\,d and vertical height h h\,h from a tracking station are modeled by the parametric equations
d=2t+54t−1,h=144t−1,t>0.25 d = \frac{2t + 5}{4t - 1}, \quad h = \frac{14}{4t - 1}, \quad t > 0.25 d=4t−12t+5,h=4t−114,t>0.25where t t\,t is the time in minutes after launch.
Show that the path of the drone lies on a straight line.
Hence, or otherwise, determine the horizontal distance d d\,d of the point where the drone's path intersects a boundary defined by the line h=3d−5h = 3d - 5h=3d−5.
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.