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The locus of any point P(z) on argand pl...

The locus of any point `P(z)` on argand plane is `arg((z-5i)/(z+5i))=(pi)/(4)`.
Then the length of the arc described by the locus of `P(z)` is

A

`62`

B

`74`

C

`136`

D

`138`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Centre `(5,0)`, radius `=5sqrt(2)`
`:.` Equation of the circle `(x-5)^(2)+y^(2)=50`
For `x=1`, `y^(2)=34`.
Total number of integral points `=(5+5+1)`.
Similarly for `x=2,3,…..12`
Finally number of integral points inside the region is `136`.
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