# The hyperbola in the plane: hyperbola

### 13.12.2 The hyperbola in the plane: hyperbola

See Section 14.11.2 for hyperbolas in space.

The hyperbola command draws hyperbolas and other conic sections.

hyperbola can take parameters in different forms.

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

  #### Example.

  Input:

  hyperbola(x^2 - 2*y^2 - 1)

  Output:

- - hyperbola can take three arguments:
    - A,B, two points.
    - C, a point or a real number.
  - hyperbola(A,B,C) returns and draws the hyperbola 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:
    hyperbola(-i,i,i+1)
    Output:
  - Input:
    hyperbola(-i,i,1/2)
    Output: