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Thread: Ellipse canonical equation

  1. #1
    Aug 2008

    Question Ellipse canonical equation

    By introducing suitable coordinate axes, show that a curve with the above “constant sum” property indeed has an equation of the form
    $\displaystyle \displaystyle{ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 }$
    (It is a good idea to start with the two square root terms, representing the distances F1 P and F2P, on opposite sides of the equation.)
    Show also that any equation of this form is obtainable by suitable choice of $\displaystyle F_1$, $\displaystyle F_2$ and $\displaystyle F_1P+F_2P$.
    I've done the non-bold part. Help me with the bold part, i.e. the any keyword.
    Last edited by courteous; Oct 1st 2010 at 02:18 AM.
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