Parametric Equations

The Parameter

Parametric equations define \(y\) and \(x\) as being dependent on the parameter \(t\) rather than on each other, but sometimes we can combine the parametric equations into a single function \(y = f(x)\) or \(x = g(y)\) showing that there is some dependent relationship between the \(x\) and \(y\) variables. We often refer to this as eliminating the parameter. Let's look at a few examples.