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If locus of point P(z) in complex plane is |z+z_(1)|+|z+z_(2)|=4 where A represents z_(1) as (1,0) and B represents z_(2) as (-1, 0) and Q(omega) is moving point inside the locus of P(z) such that all internal angle bisectors of triangle /_\PAB concurrent at Q. Then, answer the following questions if |omega-omega_(1)|+|omega-omega_(2)|=2 If minimum value fo |omega-z_(1)|+|omega-z_(2)| is equal to m, then [m] is (where [.] denotes greatest integer part)

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Solution :LOCUS of `Q` is an ellipse whose vertices `z1` and `z2` don’t lie on it and eccentricity is `sqrt(2/3)` for locus of `Q`.
Now, `2ae=2xxsqrt(2/3)`
`|z_(1)-z_(2)|=2`
`:.[m]=2( :' m LT |z_(1)-z_(2)|)`


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