# The ellipse in the plane: ellipse

### 13.12.1 The ellipse in the plane: ellipse

See Section 14.11.1 for ellipses in space.

The ellipse command draws ellipses and other conic sections.

ellipse can take parameters in different forms.

- - ellipse can take one parameter:
    eqn, a second degree equation in the variables x and y (or an expression which will be set to zero).
  - ellipse(eqn) returns and draws the conic section given by eqn.

  #### Example.

  Input:

  ellipse(x^2 + 2*y^2 - 1)

  Output:

- - ellipse can take three arguments:
    - A,B, two points.
    - C, a point or a real number.
- ellipse(A,B,C) returns and draws the ellipse with foci A and B and passing through C (if C is a point) or whose semi-major axis has length C (if C is a real number).

Note that if the third argument is a point on the real axis, the real affix of the point won’t work, it needs to be specified with the point command.

#### Examples.

- Input:
  ellipse(-i,i,i+1)
  Output:
- Input:
  ellipse(-i,i,sqrt(5) - 1)
  Output: