Equations written in terms of (x) and (y) are known as bCartesian/b equations.
For example, the general Cartesian equation for a circle with radius (r) and center at the origin is:
(x2+y2=r2)
Equations written in terms of another parameter (e.g. (t)) are known as bparametric/b equations.
For example, the general parametric equation for the above circle is:
(x=r\cos{t}, y=r\sin{t})
[b]uConversion from parametric to Cartesian[/u]/b
Substitution can be used to convert equations from parametric to Cartesian form by eliminating the parameter.
If the parametric equations involves trigonometric functions, then trigonometric identities can be used to convert from parametric to Cartesian form.
[b]uDomain and range[/u]/b
For parametric equations (x=p(t), y=q(t)) with Cartesian equation (y=f(x)):
ul
liThe domain of (f(x)) is the range of (p(t));/li
liThe range of (f(x)) is the range of (q(t))./li
/ul
Cartesian equations are expressed in terms of (x) and (y) only.
Parametric equations are expressed in terms of a parameter, e.g. (t) or (θ).
Substitution or trigonometric identities can be used to convert from parametric to Cartesian form by eliminating the parameter.