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Complex Numbers question

2023 · 25 Jan · Shift 1 · Q35

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JEE Main
Mathematics
Complex Numbers
2023 · 25 Jan · Shift 1 · Q35

Complex Numbers question

2023 · 25 Jan · Shift 1 · Q35

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

\mathrm{z_1=2+3i}

and

\mathrm{z_2=3+4i}

. The set

\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}

represents a

A
hyperbola with the length of the transverse axis 7
B
hyperbola with eccentricity 2
C
straight line with the sum of its intercepts on the coordinate axes equals $-18$
D
straight line with the sum of its intercepts on the coordinate axes equals $14$

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