The least value of p for which the two c...

The least value of p for which the two curves arg ` z= pi/6 and |z-2sqrt3i|=p` intersect is

`sqrt(3)`

`1//sqrt(3)`

`1//3`

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The correct Answer is:

The equation `|z-2sqrt(3)i|=p` represents a circle of radius p having center at C`(0,2sqrt(3))` and arg(z) `=pi//6` is a line making an angle of `30^(@)` with OX and lying in first quadrant

Let CM be perpendicular from C on OA. Then,
CM=OC`sinpi/3=2sqrt(3) xx sqrt(3)/2=3`
Clearly, the two curves will intersect, if
`CM le p rArr 3 le p rArr p ge 3`.
Hence, the least value of p is 3.

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