The parabola in the plane: parabola

### 12.12.3 The parabola in the plane: parabola

See section 13.11.3 for parabolas in space.

The parabola command draws parabolas and other conic sections.

parabola can take parameters in different forms.

- parabola can take one parameter, a second degree equation in the variables x and y (or an expression which will be set to zero).

  parabola returns and draws the conic section given by the equation.
  Input:

  parabola(x^2 - y - 1)

  Output:

- parabola can take two parameters, both points. The points will be the focus and vertex of a parabola.

  parabola returns and draws the parabola.
  Input:

  parabola(0,i)

  Output:

  Note that if the second 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.

- parabola can take two parameters, a point (a,b) and a real number c.

  parabola returns and draws the parabola y = b + c(x − a)2.
  Input:

  parabola(-i,1)

  Output:

  Input:

  parabola(-i,i,1/2)

  Output:

  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.