I've done the non-bold part. Help me with theQuote:

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 thatanyequation of this form is obtainable by suitable choice of ,and.

bold part, i.e. thekeyword.any