I've done the non-bold part. Help me with the bold part, i.e. the any keyword.By introducing suitable coordinate axes, show that a curve with the above “constant sum” property indeed has an equation of the form
(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 , and .