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if A and B are two fixed point and P moves such that angle APB =  pi by 4 then shape of locus of P will be

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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 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

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