System of equations |z + 3| - |z - 3| = 6 and |z - 4| = r, where $\mathrm{r}\in {\mathrm{R}}^{+}$ has

Equation |z + 3| - |z - 3| = 6 represents a ray to the right of complex number '3'.

|z - 4| = r represents a circle whose center is 4 and radius r.

when radius of circle r = 1, it cuts ray at two points '3' and '5'.

For radius r < 1, circle cuts ray at two points.

when radius of circle r > 1, it cuts ray at only one point.