If A and B are two fixed points and k is a fixed real number, what is the locus of point P so that PA^2+PB^2=k?

Answer 1

I know that you think your terminology/notation is clear, but to mean it is not...sorry.

Do you really mean the sum of the SQUARES of the distance from A to P and B to P.?

If what you want is the sum of the distance from A to P and the distance from B to P is fixed, the answer is an ellipse.