Hyperbola in the plane

### 26.11.2 Hyperbola in the plane

For hyperbolas in space, see Section 27.9.3.

The hyperbola command draws hyperbolas and other conic sections. hyperbola can take parameters in two different ways.

- 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.
- Alternatively, 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

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

hyperbola(-i,i,i+1)

hyperbola(-i,i,1/2)