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Given that the two curves a r g(z)=pi/6 ...

Given that the two curves `a r g(z)=pi/6 and |z-2sqrt(3)i|=r` intersect in two distinct points, then a. `[r]!=2` b. `0 < r < 3` c. `r=6` d. `3 < r < 2sqrt(3)` (Note : [r] represents integral part of r)

A

`[r] ne 2` where [.] represents greatest integer

B

`0 lt r lt 3`

C

`r = 6`

D

`3 lt r lt 2 sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, D

`CP=r,OC=2sqrt(3) , /_COP = pi//3`
`rArr Cp = OC sin .(pi)/(3)= 2sqrt(3)(sqrt(3))/(2) = 3`
Thus, when r=3, the cicle touches the line. Hencec, for two distinct points of intersection, `3ltrlt2sqrt(3)`.
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