Pure · Coordinate geometry
Chapter 1 · 4
The idea
Parametric curves
Defining a curve by parametric equations x = f(t), y = g(t), finding the coordinates of points on the curve, finding the parameter value at a given point, and reading off the range of x- and y-values from the domain of t.
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Pure · Coordinate geometry
Parametric curves
Defining a curve by parametric equations x = f(t), y = g(t), finding the coordinates of points on the curve, finding the parameter value at a given point, and reading off the range of x- and y-values from the domain of t.
Why it works
A third variable draws the curve
So far every curve has been a single equation linking and directly — a Cartesian equation like . A parametric equation describes the same sort of curve a different way: both coordinates are given separately, each as a function of a third variable called the parameter, usually :Think of t as time
At each instant the two formulas hand you an -coordinate and a -coordinate, so they hand you a point. Let run through its values and the moving point traces out the curve — exactly how you would describe the path of a thrown ball, which is why parametric equations are the natural language for motion.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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