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geometry[conic] - define a conic
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Calling Sequence
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conic(p, [A, B, C, E, F], n)
conic(p, [dir, fou, ecc], n)
conic(p, eqn, n)
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Parameters
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p
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the name of the conic
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A, B, C, E, F
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five distinct points
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dir
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the line which is the directrix of the conic
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fou
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point which is the focus of the conic
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ecc
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a positive number denoting the eccentricity of the conic
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eqn
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the algebraic representation of the conic (i.e., a polynomial or an equation)
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n
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(optional) list of two names representing the names of the horizontal-axis and vertical-axis
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Description
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A conic 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 a conic.
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from the directrix, focus, and eccentricity. The input is a list of the form [dir, fou, ecc] where dir, fou, and ecc are explained above.
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from its internal 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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The routine returns a conic which includes the degenerate cases for the given input. The output is one of the following object: (or list of objects)
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a point (ellipse: degenerate case)
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two parallel lines or a "double" line (parabola: degenerate case)
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a list of two intersecting lines (hyperbola: degenerate case)
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The information relating to the output conic p depends on the type of output. Use the routine geometry[form] to check for the type of output. For a detailed description of the conic p, use the routine detail (i.e., detail(p))
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The command with(geometry,conic) allows the use of the abbreviated form of this command.
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Examples
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define conic c1 from its algebraic representation:
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![conic(c1, x^2-2*x*y+y^2-6*x-10*y+9 = 0, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math200.png)
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![conic(c2, [l, f, e], [c, d])](/support/helpjp/helpview.aspx?si=5836/file04100/math224.png)
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![conic(c3, [A, B, C, E, F], [t1, t2])](/support/helpjp/helpview.aspx?si=5836/file04100/math239.png)
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![conic(c4, x^2-6*x+13+y^2-4*y-9, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math250.png)
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ellipse: "the given equation is indeed a circle"
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![conic(c5, x^2+y^2-4*x-10*y+29 = 0, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math264.png)
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conic: "degenerate case: single point"
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degenerate case of an ellipse
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![conic(c6, x^2-2*x*y+2*x+y^2-2*y+1, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math280.png)
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conic: "degenerate case: a double line"
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degenerate case of a parabola
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![conic(c7, x^2-2*x*y-4*x+y^2+4*y-77, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math296.png)
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conic: "degenerate case: two ParallelLine lines"
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![[Line_1_c7, Line_2_c7]](/support/helpjp/helpview.aspx?si=5836/file04100/math302.png)
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degenerate case of a parabola
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![conic(c8, 11*x^2+24*x*y+4*y^2+26*x+32*y+15 = 0, [x, y])](/support/helpjp/helpview.aspx?si=5836/file04100/math315.png)
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conic: "degenerate case: two intersecting lines"
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![[Line_1_c8, Line_2_c8]](/support/helpjp/helpview.aspx?si=5836/file04100/math321.png)
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the degenerate case of a hyperbola
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