Solution:

Let P (h, k) represent any point on the locus

And let the coordinates of A and B be given by (0, 0) and (h, 0).

Where,

PA = 3PB

Upon squaring both the sides we get,

h² + k² = 9k²

h² = 8k²

By replacing (h, k) with (x, y)

Therefore, the locus of point is x² = 8y²