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AP EAMCET201920 Apr 2019Evening ShiftMathematicsComplex NumberActual

z₁, z₂ are two complex numbers with |z₁-z₂ | < k . If the complex number z satisfies the condition |z-z₁ |+ |z-z₂ |=k , then z lies on

Options

  1. Aa parabola
  2. Ban ellipse
  3. Ca circle
  4. Da hyperbola

Correct answer

B. an ellipse

Step-by-step solution

According to the given information, |z-z₁ |+ |z-z₂ |=K> |z₁-z₂ | Sum of the distances of the point z from z₁ and z₂ is constant (K) and more than the distance between points z₁ and z₂ . So, locus of point ' z ' is an ellipse. Hence, option (b) is correct.

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