geometry[ellipse] - define an ellipse
|
Calling Sequence
|
|
ellipse(p, [A,B,C,E,F], n)
ellipse(p, ['directrix'=dir, 'focus'=fou, 'eccentricity'=ecc], n)
ellipse(p, ['foci'=foi, 'MajorAxis'=lma], n)
ellipse(p, ['foci'=foi, 'MinorAxis'=lmi], n)
ellipse(p, ['foci'=foi, 'distance'=dis], n)
ellipse(p, ['MajorAxis'=ep1, 'MinorAxis'=ep2], n)
ellipse(p, eqn, n )
|
|
Parameters
|
|
p
|
-
|
the name of the ellipse
|
A, B, C, E, F
|
-
|
five distinct points
|
'directrix'=dir
|
-
|
dir is the line which is the directrix of the ellipse
|
'focus'=fou
|
-
|
fou is a point which is the focus of the ellipse
|
'eccentricity'=ecc
|
-
|
ecc is a constant less than one denoting the eccentricity of the ellipse
|
'foci'=foi
|
-
|
foi is a list of two points which are the foci of the ellipse
|
'MajorAxis'=lma
|
-
|
where lma is the length of the major axis
|
'MinorAxis'=lmi
|
-
|
where lmi is the length of the minor axis
|
'distance'=dis
|
-
|
where dis is the sum of distance of any point on the ellipse to the foci
|
'MajorAxis'=ep1
|
-
|
where ep1 is a list of two points which is the two end points of the major axis
|
'MinorAxis'=ep2
|
-
|
where ep2 is a list of two points which is the two end points of the minor axis
|
eqn
|
-
|
the algebraic representation of the ellipse (i.e., a polynomial or an equation)
|
n
|
-
|
(optional) a list of two names representing the names of the horizontal-axis and vertical-axis
|
|
|
|
|
Description
|
|
•
|
An ellipse is the set of all points in the plane, the sum of whose distances from two fixed points is a given positive constant that is greater than the distance between the fixed points.
|
•
|
The two fixed points are called the foci.
|
•
|
An ellipse 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 an ellipse.
|
–
|
from the directrix, focus, and eccentricity. The input is a list of the form where dir, fou, and ecc are explained above.
|
–
|
from the foci, and the length of the major axis. The input is a list of the form where foi and lma are explained above.
|
–
|
from the foci, and the length of the minor axis. The input is a list of the form where foi and lmi are explained above.
|
–
|
from the foci, and the sum of distance of any point on the ellipse to the foci. The input is a list of the form where foi and dis are explained above.
|
–
|
from the end points of the major and minor axis. The input is a list of the form where ep1 and ep2 are explained above.
|
–
|
from its algebraic 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 an ellipse p, use the following function calls:
|
form(p)
|
returns the form of the geometric object (i.e., ellipse2d if p is an ellipse).
|
center(p)
|
returns the name of the center of p.
|
foci(p)
|
returns a list of two foci of p.
|
MajorAxis(p)
|
returns the length of the major axis of p.
|
MinorAxis(p)
|
returns the length of the minor axis of p.
|
Equation(p)
|
returns the equation that represents the ellipse 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 ellipse p.
|
|
|
•
|
The command with(geometry,ellipse) allows the use of the abbreviated form of this command.
|
|
|
Examples
|
|
>
|
|
define ellipse e1 from its algebraic representation:
>
|
|
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
define ellipse e2 from its foci and length of the major axis
>
|
|
>
|
|
| (4) |
define ellipse e3 from its foci and length of the minor axis
>
|
|
>
|
|
| (5) |
>
|
|
| (6) |
define ellipse e4 from its foci and the sum of distance of any point on the ellipse to the foci
>
|
|
>
|
|
| (7) |
define ellipse e5 from end points of the major and minor axis
>
|
|
>
|
|
>
|
|
| (8) |
define ellipse e6 from its directrix, focus and eccentricity:
>
|
|
>
|
|
| (9) |
|
|