Q47 / 160 · AP EAMCET 2019 (20 Apr Shift 2) · Mathematics

$z_1, z_2$ 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
  • Correct answer
    B
    an ellipse
  • C
    a circle
  • D
    a hyperbola

Solution

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 point ' $z$ ' is an ellipse. Hence, option (b) is correct.

Hence, the correct answer is option: 'B'.

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