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.
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.
