geometry[parabola] - define a parabola
|
Calling Sequence
|
|
parabola(p, [A, B, C, E, F], n )
parabola(p, ['focus'=fou, 'vertex'=ver], n )
parabola(p, ['directrix'=dir, 'focus'=fou], n )
parabola(p, eqn, n )
|
|
Parameters
|
|
p
|
-
|
the name of the parabola
|
A, B, C, E, F
|
-
|
five distinct points
|
'focus'=fou
|
-
|
fou is the point which is the focus of the parabola
|
'vertex'=ver
|
-
|
ver is the point which is the vertex of the parabola
|
'directrix'=dir
|
-
|
dir is the line which is the directrix of the parabola
|
eqn
|
-
|
the algebraic representation of the parabola (i.e., a polynomial or an equation)
|
n
|
-
|
(optional) list of two names representing the names of the horizontal-axis and vertical-axis
|
|
|
|
|
Description
|
|
•
|
A parabola is the set of all points in the plane that are equidistant from a given line and a given point not on the line. A parabola is symmetric about the line that passes through the focus at right angles to the directrix. This line, called the axis of the parabola, meets the parabola at a point called the vertex.
|
•
|
The given line is called the directrix of the parabola, and the given point the focus.
|
•
|
A parabola p can be defined as follows:
|
–
|
from five distinct points. The input is a list of five points. Note that a set of five distinct points does not necessarily define a parabola.
|
–
|
from the focus and vertex. The input is a list of the form ['focus'=fou, 'vertex'=ver] where fou and ver are explained above.
|
–
|
from the directrix and focus. The input is a list of the form ['directrix'=dir, 'focus'= fou] where dir and fou are explained above.
|
–
|
from its internal representation eqn. The input is an equation or a polynomial. If the optional argument n is not given, then:
|
–
|
if the two environment variables _EnvHorizontalName and _EnvVerticalName are assigned two names, these two names will be used as the names of the horizontal-axis and vertical-axis respectively.
|
–
|
if not, Maple will prompt for input of the names of the axes.
|
•
|
To access the information relating to a parabola p, use the following function calls:
|
form(p)
|
returns the form of the geometric object (i.e., parabola2d if p is a parabola).
|
vertex(p)
|
returns the name of the vertex of p.
|
focus(p)
|
returns the name of the focus of p.
|
directrix(p)
|
returns the name of the directrix of p.
|
Equation(p)
|
returns the equation that represents the parabola p.
|
HorizontalName(p)
|
returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.
|
VerticalName(p)
|
returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.
|
detail(p)
|
returns a detailed description of the parabola p.
|
|
|
•
|
The command with(geometry,parabola) allows the use of the abbreviated form of this command.
|
|
|
Examples
|
|
>
|
|
define parabola p1 from its algebraic representation:
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
define parabola p2 from its focus and vertex
>
|
|
>
|
|
| (4) |
define parabola p3 from its directrix and its focus
>
|
|
>
|
|
| (5) |
define parabola p4 from five distinct points
>
|
|
>
|
|
>
|
|
| (6) |
>
|
|
>
|
|
| (7) |
>
|
|
| (8) |
>
|
|
| (9) |
>
|
|
| (10) |
|
|