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1.3 Coordinate Geometry in the x-y Plane

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Question 52

The curve CCC is defined by the parametric equations

x=1t+3y=2t−1t+2t>0 x = \frac{1}{t} + 3 \quad y = \frac{2t - 1}{t + 2} \quad t > 0 x=t1​+3y=t+22t−1​t>0
a.

Show that the equation of CCC can be written in the form y=g(x)y = g(x)y=g(x) where ggg is the function

g(x)=ax+bcx+dx>k g(x) = \frac{ax + b}{cx + d} \quad x > k g(x)=cx+dax+b​x>k

where a,b,c,da, b, c, da,b,c,d and kkk are integers to be found.

[5]
b.

Hence, or otherwise, state the range of ggg.

[3]
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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