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Rearranging this formula

  1. Aug 31, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi!

    I'm reading a great book by Paul Nahin, 'Chases & Pursuits', and during one derivation he skips a few steps in rearranging a formula. I'm struggling to see exactly how it was arranged and it's really bugging me.. it can't be too difficult, I think I'm just missing a key step in the process.

    If someone would be kind enough as to give me a clue it would be much appreciated!

    Thanks in advance,
    Gus


    2. Relevant equations
    [itex]\frac{\sqrt{(x-a)^{2}+y^{2}}}{\sqrt{(x-b)^{2}+y^{2}}}=k^{2}[/itex]

    where [itex]a[/itex], [itex]b[/itex] and [itex]k[/itex] are constants.


    3. The attempt at a solution
    (or 'What it should be rearranged to')

    [itex]\left [ x-\frac{k^{2}b-a}{k^2-1}\right ]^{2}+y^{2}=\left [\frac{k(a-b)}{1-k^{2}}\right ]^{2}[/itex]
     
    Last edited: Aug 31, 2011
  2. jcsd
  3. Aug 31, 2011 #2

    SteamKing

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    What are p and m?
     
  4. Aug 31, 2011 #3
    Apologies, I wanted to change p and m from the original text to a and b... OP has been updated.
     
  5. Aug 31, 2011 #4

    SammyS

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    Start by multiplying both sides by the denominator. Then square both sides. ...
     
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