### 26.12.8 Parametric equation of a geometric object in the plane

See Section 27.10.6 for parametric equations in 3D geometry.

The parameq command finds a parametric equation for a curve.

- parameq takes C, a curve.
- parameq(C) returns a parametric equation for C, in the form x(t)+i y(t).

Note that t must be a formal variable, it may be necessary to purge it with purge(t).

#### Examples

parameq(line(-1,i))

| ⎛ ⎝ | 1+i | ⎞ ⎠ | t−1

parameq(circle(-1,i))

−1+i ei t |  |  |  |  |  |  |  |  |  |

normal(parameq(ellipse(-1,1,i)))

−2 i t2−4 t+i
2 t2+1