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Coordinate Geometry (Metric)

This class covers straight lines, circles, curves given by parametric equations and curves given by polar equations. The early topics are likely to be revision; you'll have met the later ones if you've done Further Maths or the equivalent.

Straight Lines

Gradient and intercept of a straight line. This is a Higher GCSE/A-level topic, which Science and Engineering courses at Imperial will assume you know.

The straight line \(y=m\,x+c\).

Circles

Centre and radius of a circle. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

The circle \((x-a)^2+(y-b)^2-r^2\).

Parametric Curves

Curves given by expressing \(x\) and \(y\) in terms of a parameter. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

Curves given by equations of the form \(x=f_1(t)\), \(y=f_2(t)\).

Polar Curves

Curves given by relations between the polar coordinates \(r\) and \(\theta\). This is a Further Maths topic; courses that require Further Maths may assume it.

Curves given by equations of the form \(r=f(\theta)\).