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Determine the equation of the conic section

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Asymptotes at y=±[itex]\sqrt{10}[/itex] x /5

    Foci: (±[itex]\sqrt{7}[/itex],0)


    2. Relevant equations



    3. The attempt at a solution

    It's obviously a hyperbola. What I can't wrap my head around is why a^2 + b^2 ≠ c^2

    c = sqrt 7 ; correct?

    This yields
    7=25+10
    obviously NOT true. What am I missing here?
     
    Last edited: Dec 9, 2012
  2. jcsd
  3. Dec 10, 2012 #2

    Mark44

    Staff: Mentor

    No. c = √7.

    You know that a2 + b2 = 7.

    If one vertex is at (a, 0), use the slope of the asymptote to write b in terms of a, and then solve for a. You should find that a < c.

     
  4. Dec 10, 2012 #3
    Sorry I meant c^2 = 7.

    Still. The asymptotes of a hyperbola that shoots of in the x direction is positive and negative a/b.

    I don't get this at all.
     
  5. Dec 10, 2012 #4

    Mark44

    Staff: Mentor

    If the hyperbola's vertices are at (±a, 0), the asymptotes are given by y = ±(b/a)x. What are the coordinates of the point on the line y = (b/a)x at which x = a? You are given the slope of the asymptotes, and you also know that a2 + b2 = 7.

    You have two equations that involve a and b, so you should be able to solve for these variables.
     
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