TS EAMCET · Maths · Complex Number
\(z_1, z_2\) are two fixed points on the Argand plane. If \(z\) is a complex number such that \(\left|z-z_1\right|+\left|z-z_2\right|=\lambda\), then the locus of \(z\) is
- A a circle when \(\left|z_1-z_2\right| < \lambda\)
- B a parabola when \(\left|z_1+z_2\right|=\lambda\)
- C an ellipse when \(\left|z_1-z_2\right| < \lambda\)
- D a straight line when \(\left|z_1\right|=\left|z_2\right|=\lambda\)
Answer & Solution
Correct Answer
(C) an ellipse when \(\left|z_1-z_2\right| < \lambda\)
Step-by-step Solution
Detailed explanation
We have, \(\left|z-z_1\right|+\left|z-z_2\right|=\lambda\) It is straight line when \(\left|z_1-z_2\right|=\lambda\) It is ellipse of \(\left|z_1-z_2\right| < \lambda\) Hence, option (c) is correct.
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