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I Define hyperbola

  1. Jul 3, 2016 #1
    • Circle: its a locus of a point which moves such that its distance from a fixed point is constant
    • Ellipse: its a locus of a point which moves such that its distance from two fixed point is constant.
    • These definition makes me understand How scientist/mathematican have invented these conics , so what is the best definition of hyperbola , definition which can make me understand the mathematican's approach or thinking.
  2. jcsd
  3. Jul 3, 2016 #2


    Staff: Mentor

    The difference between the distance to two fixed points: ##| \; ||PF_2|| \, - \, ||PF_1|| \; | = 2 a = const.##
  4. Jul 3, 2016 #3
    I know this definition ,but the problem ìs that how can you show that the difference between these distance will give you a two symmetric opposite curve, we can easily realise about ellipse but not with hyperbola.
  5. Jul 3, 2016 #4


    Staff: Mentor

    The symmetry comes from the absolute value. One branch for each sign of ##||PF_2|| - ||PF_1||##. For ##a=0## one gets the degenerate hyperbola, a straight, the height of a double pyramide. Maybe I didn't catch your point.
  6. Jul 3, 2016 #5


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  7. Jul 4, 2016 #6
    I think I got
  8. Jul 7, 2016 #7


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