Here is a way of solving the task algebraically:

We can use Pythagoras' rule to express the distances AP and BP in terms of x, y and a.
This gives us two equations that allows us to eliminate a and to form a single equation in x and y.

The equation can be reduced to the form shown below:
this means that P(x, y) lies on a circle with centre (72/11, 0) and radius 12x5รท11.

You might like to consider a more general version of the task, eg change the multiplier 1.2 to r, change the coordinates of B to (b, 0).
a high-res pdf file of this new GEOaa-zz task