The locus of point P must be a part of ellipse.

**Explanation:**

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 y_{2} - y_{1} /x_{2} - x_{1})

We know that angle between two intersecting lines is given by

tan ϴ = m_{2} - m_{1}/1 + m_{1}m_{2}

Now you will get the locus of P