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Locus Definition of a Parabola

A locus is a set of a points that all meet a certain condition. In the diagram below, consider the locus containing all points P meeting the conditions of the program. You may slide any of the points in the diagram and the slider in order to answer the questions following the diagram.
1) What is another name for the shape of the locus containing only the points P as shown in the diagram?
2) What do you notice about the distances between P and the focus and directrix?
3) By moving some of the points the diagram, the locus does not satisfy the definition of a function. How can you limit the diagram to make the locus satisfy the definition of a quadratic function?