If `|z|=2 and locus of `5z-1` is the circle having radius a and `z_1^2+z_2^2-2z_1z_2 cos theta=0, then |z_1|:|z_2|=` (A) a (B) 2a (C) `a/10` (D) none of these

Options

A. a:1
B. `2a:1`
C. `a:10`
D. none of these

Answer

C

Explanation

Let `omega=5z-1`. Then,
`omega+1=5z`
`rArr |omega+1|=5|z|`
`rArr |omega+|=10`
`rArr` Locus of `omega` is a circle having center at (-1,0) and radius 10
`rArr a=10`
`rArr (z_(1)/z_(2))^(2)-2(z_(1)/z_(2))costheta+1=0`
`rArr z_(1)/z_(2) = costheta+-isintheta`
`rArr |z_(1)/z_(2)|=1 rArr |z_(1)|=|z_(2)| rArr |z_(1)|:|z_(2)|=1:1=a:10`