If | z_ 1 z-z_ 2 z_ 1 z+z_ 2 |=K, K > 0 (z 1 , z 2 ≠ 0), then
Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations
If \(\left|\frac{z_{1} z-z_{2}}{z_{1} z+z_{2}}\right|=K,\)K > 0 (z1, z2 ≠ 0), then
- for k ≠ 1, locus z is a straight line
- for k ∉ {1, 0}, z lies on a circle
- for k ≠ 0, z represents a point
- for k ≠ 1, z lies on the perpendicular bisector of the line segment joining \(\frac{\mathrm{z}_{2}}{\mathrm{z}_{1}} \text { and }-\frac{\mathrm{z}_{2}}{\mathrm{z}_{1}}\).
Answer
(B) for k ∉ 1, 0 , z lies on a circle
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