If 'z' be any complex number such that |3z−2|+|3z+2|=4, then locus of 'z' is:

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A circle

An ellipse

A line segment

None of these

answer is C.

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Detailed Solution

|3z−2|+|3z+2|=4 ⇒ |z−2/3|+|z+2/3|=4/3Let z be the point P and A =23,0 ,B=-23,0 then we have PA+PB=AB. Thus P(z) is any point on the line segment AB.

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