Ellipse canonical equation

Quote:

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.