System of equaitons `|z+3|-|z-3| = 6` and `|z-4|=r` where `r in R^(+)` has

Options

A. one solution if `r gt 1`
B. one solution if `r lt 1`
C. two solutions if `r = 1`
D. at leat one solution

Answer

A, C, D

Explanation

Equation `|z+3|-|z-3|= 6` represent a ray to the right of complex number '3'.
`|z-4|= r` represents a circle whose centre is 4 and radius r.

When radius of circle =1,it cuts ray at two point '3' and '5'
For radius `r le 1`, circle cuts ray at two points.
When radius of circle `r gt 1`, it cuts raty at only one point .