# Ellipse canonical equation

• September 30th 2010, 10:10 AM
courteous
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
$\displaystyle{ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 }$
(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 $F_1$, $F_2$ and $F_1P+F_2P$.
I've done the non-bold part. Help me with the bold part, i.e. the any keyword.