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I have sliced a cone with a plane mentally in every way that I can think of, and cannot figure out how parallel lines may be achieved. ... Date: 03/05/98 at 17:47:12 From: Doctor Sam Subject: Re: Conic Sections Hi, As far as I know, there are only three degenerate conics: a point, a line, and a pair of intersecting lines.
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mathforum.org/library/drmath/view/54458.html
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If it does pass through the vertex, the following degenerate conics will be produced: A hyperbola will degenerate into two intersecting lines. Imagine sliding the plane to the left and try to visualize the result on ... Two parallel lines are produced when the plane is parallel to the central axis and cuts through twice.
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www.bmlc.ca/PureMath30/Pure%20Math%2030%20-%20Conics%20...
www.bmlc.ca/PureMath30/Pure%20Math%2030%20-%20Conics%20Lesson%201.pdf
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Conic section - Wikipedia, the free encyclopedia
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In mathematics, a conic section (or just conic ) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be de...
en.wikipedia.org/wiki/Conic_section
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Parallel Lines x2-1=0 Imaginary Parallel Lines x2+1=0 ... The type VII linear system has only real degenerate conics, which are pairs of lines, one of which is a line of base points. There is also one real base point not on that line.
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www.ipfw.edu/math/Coffman/pov/lsoc.html
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An additional feature, unique to the hyperbola amongst the conics, ... A degenerate conic equation in the form of a circle or ellipse can produce a graph consisting of one point or no points. A degenerate conic equation in the form of a parabola can produce a graph consisting of a pair of parallel lines, one line, or no points.
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web.gsc.edu/fs/thartfield/courses/2009-3-fall/1113-Coni...
web.gsc.edu/fs/thartfield/courses/2009-3-fall/1113-Conic_Sections.pdf
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write Z for the set of lines of 9(~K ). Let F be a degenerate conic of 9(SK). ..... parallel to the line x~Z(K) w i t h .x ~ g i v e n b y (9). ...
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www.springerlink.com/index/P26V786613508832.pdf
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d affects the scaling or size of the curve, except when d == 0 we get a degenerate conics. The magnitude of d is proportional to the size of the curve. We have the following cases: ... Both observations are correct, but in projective geometry parallel lines are said to meet at infinity. This convention reduces wordiness...
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xahlee.org/SpecialPlaneCurves_dir/ConicSections_dir/con...
xahlee.org/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html
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Conversely, every quadratic equation represents a conic, be it that it can be degenerate: either in two (intersecting or parallel) lines, or in two coincident lines. ... This constructor can only be used for non-degenerate, real conics: If the centre point c is a finite point and rx and ry have the same sign,
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www.lems.brown.edu/vision/vxl_doc/html/core/vgl/html/cl...
www.lems.brown.edu/vision/vxl_doc/html/core/vgl/html/classvgl__conic.html
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Degenerate Conic Sections ... When a plane is parallel to the bases of two cones and slices the cones at their intersection, a circle is not formed. ... The hyperbola degenerates into 2 lines.
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www.fortbend.k12.tx.us/mastersonline/ft_bend_isd/6306/D...
www.fortbend.k12.tx.us/mastersonline/ft_bend_isd/6306/DHS/Project/Conics/degenerate.htm
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