`|(Z_1 - 1)/(Z_1 - 4)| = 2 & | (Z_2 - 4)/ (Z_2 - 1)| = 2` the `|Z_1 - Z_2|_max - |Z_1 + Z_1|_min` = ?

Options

A. 2
B. 3
C. 5
D. 10

Explanation

`z_(1)` lies on the circle `(x-1)^(2)+y^(2)=4((x-4)^(2)+y^(2))rArrx^(2)+y^(2)-10x+21=0`
`z_(2)` lies on the circle `(x-4)^(2)+y^(2)=4((x-1)^(2)+y^(2))rArr x^(2)+y^(2)=4`
`|z_(1)-z_(2)|_("min")=1`, (when `z_(1)=3` and `z_(2)=2`)
`|z_(1)-z_(2)|_("max")=9` (when `z_(1)=7` and `z_(2)=-2`)
`:. |z_(1)-z_(2)|_("min")+|z_(1)-z_(2)|_("max")=10`.