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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 7

A precision-engineered micro-shuttle follows a path CCC in a magnetic field. The position of the shuttle at time ttt, where ttt is a parameter in radians, is given by the parametric equations

x=4cos⁡2t,y=8sin⁡3t,−π2<t<π2 x = 4 \cos 2t, \quad y = 8 \sin^3 t, \quad -\frac{\pi}{2} < t < \frac{\pi}{2} x=4cos2t,y=8sin3t,−2π​<t<2π​

The shuttle passes through point PPP when t=π6t = \frac{\pi}{6}t=6π​.

The line lll represents the tangent to the shuttle's path at point PPP.

a.

Use parametric differentiation to show that (i) dydx=ksin⁡t\frac{\mathrm{d}y}{\mathrm{d}x} = k \sin tdxdy​=ksint where kkk is a constant to be found. (ii) an equation for the tangent line lll is 3x+4y−10=03x + 4y - 10 = 03x+4y−10=0.

[7]
b.

The path CCC is intersected again by the line lll at the point QQQ.

Using algebra and showing detailed reasoning, find the exact coordinates of QQQ.

[6]
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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