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Question: Answered & Verified by Expert
Let $z_{1}, z_{2}$ be two fixed complex numbers in the argand plane and $z$ be an arbitrary point satisfying $\left|z-z_{1}\right|+\left|z-z_{2}\right|=2\left|z_{1}-z_{2}\right|$. Then, the locus of $z$ will be
MathematicsComplex NumberWBJEEWBJEE 2014
Options:
  • A an ellipse
  • B a straight line joining $z_{1}$ and $z_{2}$
  • C a parabola
  • D a bisector of the line segment joining $z_1$ and $z_2$
Solution:
1225 Upvotes Verified Answer
The correct answer is: an ellipse
We know that $\left|z-z_{1}\right|+\left|z-z_{2}\right|=k$ will represent an ellipse, if $\left|z_{1}-z_{2}\right| < k$
Hence. the equation $\left|z-z_{1}\right|+\left|z-z_{2}\right|$ $=2\left|z_{1}-z_{2}\right|$ represent an ellipse.

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