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1.3 Coordinate Geometry in the x-y Plane

1.3 Coordinate Geometry in the x-y Plane

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Question 68

A research drone is programmed to follow a specific surveillance path during a flight test. Its position (x,y)(x, y)(x,y) in kilometers relative to a base station at time t t\,t is given by the parametric equations

x=4sec⁡tandy=7tan⁡twhere 0≤t<π2 x = 4\sec t \quad \text{and} \quad y = 7\tan t \quad \text{where } 0 \le t < \frac{\pi}{2} x=4sectandy=7tantwhere 0≤t<2π​

Which of the options shown below is a Cartesian equation for the drone's path?

x216+y249=1\frac{x^2}{16} + \frac{y^2}{49} = 116x2​+49y2​=1

49x2−16y2=78449x^2 - 16y^2 = 78449x2−16y2=784

16x2−49y2=78416x^2 - 49y^2 = 78416x2−49y2=784

x2−y2=33x^2 - y^2 = 33x2−y2=33

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Markscheme

1.3 Coordinate Geometry in the x-y Plane Questions

  1. A Level
  2. /Maths
  3. /1.3 Coordinate Geometry in the x-y Plane

143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.

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