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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 24

The curve C C\,C has parametric equations

x=t2−4x = t^2 - 4x=t2−4, y=t3−4ty = t^3 - 4ty=t3−4t, t∈Rt \in \mathbb{R}t∈R

a.

Show that C C\,C crosses itself at the origin, and state the two values of t t\,t for which C C\,C passes through the origin.

[4]
b.

Find an equation of the tangent to C C\,C at the point where t=2t = 2t=2.

[3]
c.

Hence write down an equation of the other tangent to C C\,C at the origin.

[1]
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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