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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

`10sqrt(2)pi`

B

`(15pi)/(sqrt(2))`

C

`(5pi)/(sqrt(2))`

D

`5sqrt(2)pi`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)`
Given `/_APB=pi//4implies/_AOB=pi//2`
Let `OA=OB=R=` radius of the circle
`implies 2R^(2)=10^(2)impliesR=5sqrt(2)`
Length of the arc `=5sqrt(2)xx(3pi)/(2)`
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