AP EAMCET · Maths · Complex Number
\(z_1, z_2\) are two complex numbers with \(\left|z_1-z_2\right| < k\). If the complex number \(z\) satisfies the condition \(\left|z-z_1\right|+\left|z-z_2\right|=k\), then \(z\) lies on
- A a parabola
- B an ellipse
- C a circle
- D a hyperbola
Answer & Solution
Correct Answer
(B) an ellipse
Step-by-step Solution
Detailed explanation
According to the given information, \[ \left|z-z_1\right|+\left|z-z_2\right|=K>\left|z_1-z_2\right| \] \(\Rightarrow\) Sum of the distances of the point \(z\) from \(z_1\) and \(z_2\) is constant \((K)\) and more than the distance between points \(z_1\) and \(z_2\). So, locus of…
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