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The region of argand diagram defined by ...

The region of argand diagram defined by `|z-1|+|z+1|<=4 ` (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these

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`|z-1|+|z+1| le 4` shows that distance of `z` from a point `(-1,1)` is constant that is less than or equal to `4`.
So, this is the case of ellipse as in case of ellipse distance of a point from two focii is always constant.
As constant value is `4` or less than `4`, it will include the region interior of the ellipse also.
So, option `(3)` is the correct option.
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