The locus of point P must be a part of ellipse.
Take any numerical coordinates of point A and B and coordinates of point P as (h,k).
Now find the slope of both the line AP and BP (by the formula y2 - y1 /x2 - x1)
We know that angle between two intersecting lines is given by
tan ϴ = m2 - m1/1 + m1m2
Now you will get the locus of P