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Question
The region of argand plane defined by |z+1|+|z-1|≤4 is
The region of argand plane defined by |z+1|+|z-1|≤4 is
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Solution
The correct option is B Interior and boundary of ellipse
As |z- a| + |z + a| = 2b
represents set of z, sum of whose distances from (a,0) and (-a,0) is 2b and it will be an ellipse if 2a < 2b. In the question a = 1 and b = 2,
∴2a<2b
Hence |z - 1| + |z + 1| ≤ 4
Interior and boundary of ellipse
As |z- a| + |z + a| = 2b
represents set of z, sum of whose distances from (a,0) and (-a,0) is 2b and it will be an ellipse if 2a < 2b. In the question a = 1 and b = 2,
∴2a<2b
Hence |z - 1| + |z + 1| ≤ 4
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