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1.6 C: Coordinate geometry in the (x, y) plane

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Question 90

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≠14 X = \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.

a.

Show that the robotic arm moves along a straight line.

[4]
b.

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.

[3]

1.6 C: Coordinate geometry in the (x, y) plane Questions

  1. A Level
  2. /Maths
  3. /1.6 C: Coordinate geometry in the (x, y) plane

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.

Question bank