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Hyperbole question

  1. Feb 19, 2007 #1
    the formula of the hyperbole is x^2 -3*y^2=3.

    find a dot on the hyperbole that the sum of the distances
    between the dot and the focus points equals to 6

    i devided all the formula by 3 in order to find a^2 ,b^2
    i found the focus point by the formula c^2=a^2 +b^2

    the problem is the the definision of the hyperbole
    is that the subtraction of distances from every point to
    the focus point equals to 2a

    there is no law about the sum of the distances?

    only the law i mentioned before deals with them

    the answer in the book (+-3:+-2)

    plz help
     
    Last edited: Feb 19, 2007
  2. jcsd
  3. Feb 19, 2007 #2

    Dick

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    Sure. Sum of the distances=6 would define an ellipse. So you want to find a point that is both on this ellipse and your original hyperbola. Sounds like an intersection problem to me.
     
  4. Feb 19, 2007 #3
    no ellipse involved i know that a sum of distances is an ellipse definition

    but there is no ellipse here
     
  5. Feb 19, 2007 #4

    Dick

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    My suggestion was to put an ellipse into the problem! The one defined by sum of the focal distances = 6. That will give you a second equation in x,y to intersect with your hyperbola.
     
  6. Feb 19, 2007 #5
    i didnt understand
    if i will create such an ellipse ,
    it will mean that 2a=6 a=3
    thats will leave me B unknown for this ellipse??

    and even if i some how find B
    does these shared points will be these points we are looking for??
     
    Last edited: Feb 19, 2007
  7. Feb 19, 2007 #6

    Dick

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    You know the foci of the ellipse (they are the same as the hyperbola). You know the sum of the focal distances (6). Isn't that enough to write down an equation for the ellipse?
     
  8. Feb 19, 2007 #7
    even if we put the same foci and we will find this ellipse
    why the should shared points of the given hyperbole and this ellipse
    represent the points we are looking for??
     
    Last edited: Feb 19, 2007
  9. Feb 19, 2007 #8

    Dick

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    The shared points will be both on the hyperbola and have the sum of the focal distances = 6 (since they are on the ellipse). Isn't that what you want?
     
  10. Feb 19, 2007 #9
    ahhhhhhhh ok
    thanks
     
  11. Feb 20, 2007 #10

    Curious3141

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    This is the zillionth time I've seen hyperbola misspelled hyperbole! The zillionth I tells ya! :tongue:
     
  12. Feb 20, 2007 #11
    in the dictionary it says hyperbole
     
  13. Feb 20, 2007 #12

    Dick

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    There are two different words. Hyperbola is the geometric figure, hyperbole (pronounced like hyper-bolee) means an exaggeration or overstatement. French/latin etc use hyperbole for the geometric figure. Hyperbolic can refer to both. Fascinating!
     
  14. Feb 20, 2007 #13

    Dick

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    BTW, a statement can be elliptical or circular as well. Don't be confused!
     
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