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Math Help - Hyperbola - Loran - Rotate axis

  1. #1
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    Hyperbola - Loran - Rotate axis

    I'm trying to formulate a problem related with the Long Range Navigation(LORAN) System, that uses Hyperbolas to determine the position of a reciever(a ship for example). The Loran uses 1 master station and 2 slaves(and calculates de equation of the Hyperbola betwin the master and each of the slave stations) and if the stations are aligned at a 90 degree angle it's not hard to determine the equation for the 2 hyperbolas.
    With the distance from point P to stations A and C, and the distance from A to C I can get the first equation, and doing the same to stations A and C I can the second equation and solve for x and y.(C is the master)

    (x/a)^2 - (y/b)^2=1 (for an horizontal hyperbola)

    My problem is when these stations aren't perfectly aligned. I'm not getting how i can incorporate the rotation of the hyperbola.Is there a equation for the Hyperbola when the axis is rotated ( I know i have to have some x*y in the equation but i can't figure it out). I attached a pic with what I'm looking for.
    Nando
    Attached Thumbnails Attached Thumbnails Hyperbola - Loran - Rotate axis-untitled.jpg  
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  2. #2
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    Re: Hyperbola - Loran - Rotate axis

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