If the equation |z−a|+|z−b|=3 represents an ellipse and a,b∈R, (where a is fixed point), then b lies
A
Outside the circle |z−a|=3
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B
Inside the circle |z−a|=3
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C
On the circumference of the circle |z−a|=3
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D
None of these
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Solution
The correct option is B Inside the circle |z−a|=3 |z−a|+|z−b|=3 represents an ellipse. Now |a−b|<3 ⇒|b−a|<3 Let locus of bbeα ⇒|α−a|<3 Which represents region inside the circle having centre at a and radius 3 units.