WBJEE · Maths · Complex Number
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
- 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 \(z_2\)
Answer & Solution
Correct Answer
(A) an ellipse
Step-by-step Solution
Detailed explanation
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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