posted by Daksh .
Find the equation of the locus of the point representing z if |z-5-12i| + |z-5+21i|=13
|z-5-12i| + |z-5+12i|=13
|z-5-12i| is the distance of z from 5+12i
|z-5+12i| is the distance of z from 5-12i
As we know, the locus of a point whose distances from two other points add to a constant, is an ellipse.
The equation of the ellipse should be no problem, since you know the foci and the sum of the distances.