The flight path of a surveillance drone in a vertical cross-section is modelled by the parametric equations x=2t2−16t,y=t3−16t,t∈Rx = 2t^2 - 16t, \quad y = t^3 - 16t, \quad t \in \mathbb{R}x=2t2−16t,y=t3−16t,t∈R where x x\,x represents the horizontal displacement from a control tower and y y\,y represents the height relative to a safety baseline. The drone's path crosses the baseline at the origin and at the points A A\,A and BBB, where A A\,A and B B\,B are distinct points.
Find the coordinates of A A\,A and show that B B\,B has coordinates (96,0)(96, 0)(96,0).
Show that the equation of the tangent to the path at B B\,B is x+y−96=0x + y - 96 = 0x+y−96=0
The tangent to the path at B B\,B intersects the path again at the point PPP.
Find, using algebraic methods, the horizontal displacement of the drone at point PPP.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) 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.