1.

Equation of the circles |z-1-i|=1 & |z-1+i|=1 touches internally a circle of radius 2. The equation of the circle touching all the circles can be

Answer»

`3zbarz+z+barz-1=0`
`3zbarz-7(z+barz)+15=0`
`zbarz-z-barz-3=0`
`3zbarz+(z+barz)+1=0`

Solution :GIVEN circle touches externally at real AXIS So, the centre `C` of the DESCRIBED circles lies on real axis which has radius `R` then `"CC"_(1)="CC"_(2)=1+r`
`C_(1)C_(3)=C_(2)C_(3)=1`
`"CC"_(3)=2-r`
`:.(1+r)^(2)=1^(2)+(2-r)^(2)`
`impliesr=2//3`
`:.` Centre of described circle is
`-1+2/3=(-1)/3` or `3-2/3=7/3`

`:.` Required equation of circle are
`|z+1/3|=2/3` & `|z-7/3|=2/3`


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