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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 69

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

1.5 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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