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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 71

The movement of a precision robotic arm across a flat surface is defined by the parametric relationship

x=6cos⁡2y0≤x≤6,0≤y≤π4 x = 6 \cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4} x=6cos2y0≤x≤6,0≤y≤4π​

where xxx is the horizontal position in millimetres and yyy is the control angle in radians.

a.

Find dxdy\frac{dx}{dy}dydx​ in terms of yyy.

[2]
b.

Hence show that

dydx=k36−x2 \frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}} dxdy​=36−x2​k​

where kkk is a constant to be found.

[3]
c.

A specific calibration point P(a,b)P(a, b)P(a,b) lies on the path of the arm. Given that

  • the gradient of the path at PPP is −16-\frac{1}{6}−61​
  • both aaa and bbb are positive constants

find the exact values of aaa and bbb.

[4]
Markscheme

1.5 Coordinate Geometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Coordinate Geometry

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.

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