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Centre and radius of the circle |z - a| = k|z - b|

This type of question, asked 3 times: 25 Jan 2023, 1 Feb 2023, 23 Jan 2025. All 3 questions below, oldest first.

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  1. Question 1

    25 Jan 2023

    166
    Let zz be a complex number such that ∣z−2iz+i∣=2,z≠−i\left| \frac{z - 2i}{z + i} \right|= 2,z \neq - i. Then zz lies on the circle of radius 2 and centre

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  2. Question 2

    1 Feb 2023

    78
    If the center and radius of the circle ∣z−2z−3∣=2\left| \frac{z - 2}{z - 3} \right|= 2 are respectively (α,β)(\alpha,\beta) and γ\gamma. then 3(α+β+γ)3(\alpha + \beta + \gamma) is equal to

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  3. Question 3

    23 Jan 2025

    60
    Let ∣zˉ−i2z‾+i∣=13,z∈C\left| \frac{\bar{z}- i}{2\overline{z}+ i} \right|=\frac{1}{3},z \in\mathbb{C}, be the equation of a circle with center at C . If the area of the triangle, whose vertices are at the points (0,0),C(0,0),C and (α,0)(\alpha,0) is 11 square units, then α2\alpha^{2} equals

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