Pure · Coordinate geometry
Chapter 1 · 4
The idea
Modelling with parametric equations
Using parametric equations to model real situations where x and y each depend on time — projectiles and rotating points — reading positions, maxima and ranges from the model, and finding the Cartesian equation of the path.
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Pure · Coordinate geometry
Modelling with parametric equations
Using parametric equations to model real situations where x and y each depend on time — projectiles and rotating points — reading positions, maxima and ranges from the model, and finding the Cartesian equation of the path.
Why it works
When the parameter really is time
Parametric equations earn their keep in modelling, because in the real world horizontal and vertical position are usually separate functions of time. A single Cartesian equation hides the time information; the parametric form keeps it, so you can answer "where is it?" and "when?" in the same breath. Here the parameter genuinely is time (seconds), and , are positions (metres).Reading the model
Most questions are substitution in disguise, and each phrasing points at one move:Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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