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geometry[ellipse] - define an ellipse
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Calling Sequence
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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 )
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Parameters
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p
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the name of the ellipse
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A, B, C, E, F
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five distinct points
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'directrix'=dir
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dir is the line which is the directrix of the ellipse
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'focus'=fou
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fou is a point which is the focus of the ellipse
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'eccentricity'=ecc
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ecc is a constant less than one denoting the eccentricity of the ellipse
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'foci'=foi
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foi is a list of two points which are the foci of the ellipse
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'MajorAxis'=lma
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where lma is the length of the major axis
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'MinorAxis'=lmi
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where lmi is the length of the minor axis
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'distance'=dis
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where dis is the sum of distance of any point on the ellipse to the foci
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'MajorAxis'=ep1
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where ep1 is a list of two points which is the two end points of the major axis
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'MinorAxis'=ep2
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where ep2 is a list of two points which is the two end points of the minor axis
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eqn
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the algebraic representation of the ellipse (i.e., a polynomial or an equation)
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n
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(optional) a list of two names representing the names of the horizontal-axis and vertical-axis
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Description
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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.
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The two fixed points are called the foci.
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An ellipse p can be defined as follows:
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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.
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from the directrix, focus, and eccentricity. The input is a list of the form ![['directrix' = dir, 'focus' = fou, 'eccentricity' = ecc]](/support/helpjp/helpview.aspx?si=5837/file04109/math216.png) where dir, fou, and ecc are explained above.
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from the foci, and the length of the major axis. The input is a list of the form ![['foci' = foi, 'MajorAxis' = lma]](/support/helpjp/helpview.aspx?si=5837/file04109/math226.png) where foi and lma are explained above.
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from the foci, and the length of the minor axis. The input is a list of the form ![['foci' = foi, 'MinorAxis' = lmi]](/support/helpjp/helpview.aspx?si=5837/file04109/math234.png) where foi and lmi are explained above.
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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 ![['foci' = foi, 'distance' = dis]](/support/helpjp/helpview.aspx?si=5837/file04109/math242.png) where foi and dis are explained above.
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from the end points of the major and minor axis. The input is a list of the form ![['MajorAxis' = ep1, 'MinorAxis' = ep2]](/support/helpjp/helpview.aspx?si=5837/file04109/math250.png) where ep1 and ep2 are explained above.
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from its algebraic representation eqn. The input is an equation or a polynomial. If the optional argument n is not given, then:
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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.
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if not, Maple will prompt for input of the names of the axes.
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To access the information relating to an ellipse p, use the following function calls:
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form(p)
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returns the form of the geometric object (i.e., ellipse2d if p is an ellipse).
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center(p)
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returns the name of the center of p.
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foci(p)
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returns a list of two foci of p.
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MajorAxis(p)
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returns the length of the major axis of p.
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MinorAxis(p)
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returns the length of the minor axis of p.
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Equation(p)
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returns the equation that represents the ellipse p.
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HorizontalName(p)
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returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.
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VerticalName(p)
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returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.
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detail(p)
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returns a detailed description of the ellipse p.
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The command with(geometry,ellipse) allows the use of the abbreviated form of this command.
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Examples
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define ellipse e1 from its algebraic representation:
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![center_e1, [1, -2]](/support/helpjp/helpview.aspx?si=5837/file04109/math365.png)
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![[foci_1_e1, foci_2_e1], [[1, -2-3^(1/2)], [1, -2+3^(1/2)]]](/support/helpjp/helpview.aspx?si=5837/file04109/math372.png)
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define ellipse e2 from its foci and length of the major axis
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![ellipse(e2, ['foci' = foci(e1), 'MajorAxis' = MajorAxis(e1)])](/support/helpjp/helpview.aspx?si=5837/file04109/math385.png)
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define ellipse e3 from its foci and length of the minor axis
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![ellipse(e3, ['foci' = foci(e1), 'MinorAxis' = MinorAxis(e1)])](/support/helpjp/helpview.aspx?si=5837/file04109/math398.png)
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![center_e2, [1, -2]](/support/helpjp/helpview.aspx?si=5837/file04109/math405.png)
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define ellipse e4 from its foci and the sum of distance of any point on the ellipse to the foci
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![ellipse(e4, ['foci' = foci(e1), 'distance' = 2*sqrt(6)])](/support/helpjp/helpview.aspx?si=5837/file04109/math418.png)
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define ellipse e5 from end points of the major and minor axis
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![ellipse(e5, ['MajorAxis' = [A, B], 'MinorAxis' = [E, F]])](/support/helpjp/helpview.aspx?si=5837/file04109/math435.png)
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define ellipse e6 from its directrix, focus and eccentricity:
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![ellipse(e6, ['directrix' = l, 'focus' = f, 'eccentricity' = e], [c, d])](/support/helpjp/helpview.aspx?si=5837/file04109/math454.png)
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| (9) |
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