Parametric equations

By Martin McBride, 2020-09-12
Tags: parametric equation
Categories: coordinate systems pure mathematics


We often define a curve by expression $x$ as a function of $y$:

$$y = f(x)$$

Using parametric equations we define the $x$ and $y$ coordinates of the points on the curve in terms of an independent variable, which we will call $t$:

$$ \begin{align} x = g(t)\newline y = h(t) \end{align} $$

For any value of $t$, a value of $x$ and $y$ can be calculated, and the point $(x, y)$ will lie on the curve.

One way to think of this is to imagine $t$ representing time. As the time changes, the point $(x, y)$ will move, tracing the curve. But this is just an aid to understanding, the parameter $t$ does not necessarily represent time.

In this section we will look at the parametric equations of parabolas and hyperbolas, and also see how to express them as Cartesian equations.

See also



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