The path of a robotic arm in a two-dimensional manufacturing grid (X,Y)(X, Y)(X,Y) is defined by the parametric equations
X=2p−51−4p,Y=121−4p,p≠14X = \frac{2p - 5}{1 - 4p}, \quad Y = \frac{12}{1 - 4p}, \quad p \neq \frac{1}{4}X=1−4p2p−5,Y=1−4p12,p=41
where p p\,p is a control parameter.
Show that the robotic arm moves along a straight line.
The arm's path intersects a safety perimeter defined by the line Y=3X+10Y = 3X + 10Y=3X+10. Determine the XXX-coordinate of this point of intersection.
Practise Edexcel A Level Maths 8.1 Parametric Equations with exam-style questions for A Level Maths. 20 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.