# The parametric equation of a geometric object in the plane: parameq

### 13.13.8 The parametric equation of a geometric object in the plane: parameq

See Section 14.12.6 for parametric equations in three-dimensional geometry.

The parameq command finds a parametric equation for a curve.

- parameq takes one argument:
  C, a curve.
- parameq(G) returns a parametric equation for G, in the form x(t) + iy(t).

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

#### Examples.

- Input:
  parameq(line(-1,i))
  Output:

  ⎛ ⎝ | 1+i | ⎞ ⎠ | t−1

- Input:
  parameq(circle(-1,i))
  Output:

  −1+i ei t

- Input:
  normal(parameq(ellipse(-1,1,i)))
  Output:

  −2 i t2−4 t+i
  2 t2+1