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Conic sections

  1. May 10, 2008 #1
    how do we define the eccenticity of a pair of straight lines
     
  2. jcsd
  3. May 10, 2008 #2

    Vid

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    Eccentricity is a property of conic sections. Two lines do not a conic section make.
     
  4. May 10, 2008 #3

    Vid

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  5. May 10, 2008 #4
    but i have read that pair of straight lines is a part of a conic section. how do u define a conic section.
     
  6. May 10, 2008 #5

    symbolipoint

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    Which kind of "pair of lines" do you mean? A pair of intersecting lines can be a conic section (but does this then have an eccentricity?)
     
  7. May 10, 2008 #6
    yes.
     
  8. May 10, 2008 #7

    HallsofIvy

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    x2/a^2- y2/b^2= 0 is a "degenerate" conic section. It is the limiting case of then hyperbola x2/a2c- y2/a2c= 1 or x2/a2- y2/b2= c as c goes to 0 and, since it can be factored as (x/a- y/b)(x/a+ y/b)= 0, its graph is the two lines x/a- y/b= 0 and x/a+ y/b= 0.

    The eccentricy of such a hyperbola is [tex]\sqrt{ca^2- cb^2}{ca}= \sqrt{a^2- b^2}{\sqrt{c}a}[/tex]. As c goes to 0 that goes to 0. Strictly speaking the eccentricity of a degenerate hyperbola is "not defined" but roughly speaking it is infinity.
     
  9. May 10, 2008 #8

    Hurkyl

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    I think you have the wrong formula for the eccentricity.
     
  10. May 10, 2008 #9
    then what is the correct answer
     
  11. May 10, 2008 #10

    HallsofIvy

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    Just bad "LaTex". I had meant
    [tex]\frac{\sqrt{ca^2- cb^2}}{ca}= \frac{\sqrt{a^2- b^2}}{\sqrt{c}a}[/tex]
    and the result is the same as before.
     
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