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Find the equation of hyperbola

  1. Jan 5, 2013 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    From the point (2√2,1) a pair of tangents are drawn to [itex]\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2} = 1,[/itex] which intersect the coordinate axes in concyclic points . If one of the tangents is inclined at an angle of [itex]tan^{-1}\frac{1}{√2}[/itex] with the transverse axis of the hyperbola , then find the equation of
    i) hyperbola ii)circle formed using concyclic points

    2. Relevant equations

    3. The attempt at a solution
    Equation of tangent
    [itex]y=mx+\sqrt{a^2m^2-b^2}[/itex]
    where m = [itex]tan^{-1}\frac{1}{√2}[/itex]
    Passing it through the given point will give me an equation in a and b. But there are two unknowns.
     
  2. jcsd
  3. Jan 5, 2013 #2
    Condition for tangency is ##c^2=a^2m^2-b^2##. Can you find c?

    edit: sorry didn't see that you already did this. I think you have to use the fact that the points are concyclic, or find the equation of the other tangent.
     
    Last edited: Jan 5, 2013
  4. Jan 6, 2013 #3

    utkarshakash

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    But how?
     
  5. Jan 7, 2013 #4
    I think some data might be missing. All I can think of is that the slope of the tangent is -B/A where A and B represent the intercepts of this tangent. A relation between A and B can be found by looking at the circle formed by the points of the intercept, as they are at equal distances from the centre...but the centre is not known too..
     
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