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JEE Main 202624 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2026 · 24 January · Morning Shift · Mathematics · Circle

Let S=\ z ∈ ℂ:|(z-6 i)/(z-2 i)|=1. and .|(z-8+2 i)/(z+2...

Let S={z∈C:∣z−6iz−2i∣=1 and ∣z−8+2iz+2i∣=35}\mathrm{S}=\left\{z \in \mathbb{C}:\left|\frac{z-6 i}{z-2 i}\right|=1\right.\text{ and } \left.\left|\frac{z-8+2 i}{z+2 i}\right|=\frac{3}{5}\right\}.
Then $\sum_{z \in \mathrm{~s}}|z|^{2} is equal to

Options

  1. A385
  2. B398
  3. C413
  4. D423

Correct answer

A. 385

Step-by-step solution

Solving ∣z−6iz−2i∣=1⇒y=4\left| \dfrac{z - 6i}{z - 2i} \right| = 1 \Rightarrow y = 4 .....(1)
(where z=x+iyz = x + iy)
Now solving \left| \dfrac{z - 8 + 2i}{z + 2i} \right| = \dfrac{3}{5}<br><br>\Rightarrow x^2 + y^2 - 25x + 4y + 104 = 0.....(2)<br>Solving (1) & (2)\Rightarrow z = 17 + 4i&8 + 4i<br><br>\Rightarrow \sum |z|^2 = (17)^2 + (4)^2 + (8)^2 + (4)^2 = 385
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