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Question
Assertion :Number of solutions of complex number z satisfying |z−1−2i|=|z−2−3i|=|z−3| is one Reason: If z1≠z2≠z3, then |z−z1|=|z−z2|=|z−z3| has one solution.
Assertion :Number of solutions of complex number z satisfying |z−1−2i|=|z−2−3i|=|z−3| is one Reason: If z1≠z2≠z3, then |z−z1|=|z−z2|=|z−z3| has one solution.
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Solution
The correct option is C Assertion is correct but Reason is incorrect
Locus of z satisfying
|z−1−2i|=|z−2−3i|=|z−3|
will be the circumcentre of triangle with vertices (1,2),(2,3),(3,0)
where
as |z−z1|=|z−z2|=|z−z3| can have no solution when z1,z2,z3 are collinear.
Locus of z satisfying
|z−1−2i|=|z−2−3i|=|z−3|
will be the circumcentre of triangle with vertices (1,2),(2,3),(3,0)
where
as |z−z1|=|z−z2|=|z−z3| can have no solution when z1,z2,z3 are collinear.
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