Assumed knowledge

• Familiarity with the coordinate plane.
• Facility with algebra — see the module Algebra review.
• Knowledge of elementary trigonometry.

Motivation

Coordinate geometry is where algebra meets geometry. In secondary school mathematics, most coordinate geometry is carried out in the coordinate plane \(\mathbb{R}^2\), but three-dimensional geometry can also be studied using coordinate methods.

Classical Euclidean geometry is primarily about points, lines and circles. In coordinate geometry, points are ordered pairs \((x,y)\), lines are given by equations \(ax+by+c=0\) and circles by equations \((x-a)^2+(y-b)^2=r^2\). Thus the simplest, most useful and most often met application of coordinate geometry is to solve geometrical problems. Parabolas, ellipses and hyperbolas also regularly arise when studying geometry, and we shall discuss their equations in this module.

Readers not familiar with coordinate geometry may find the TIMES module Introduction to coordinate geometry (Years 9–10) useful as a gentle introduction to some of the ideas in this module.

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