Verified Solution • 2025–26 Session moderate

QJEEM23Ma1495: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1495 Solution: Let and . The set represents a

Let z1=2+3i\mathrm{z_1=2+3i} and z2=3+4i\mathrm{z_2=3+4i} . The set S={z∈C:∣z−z1∣2−∣z−z2∣2=∣z1−z2∣2}\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

Multiple Choice Options

  • 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 −18-18
  • D straight line with the sum of its intercepts on the coordinate axes equals 1414

Step-by-Step Verified Solution

∣z−z1∣2−∣z−z2∣2=∣z1−z2∣2\left|z-z_{1}\right|^{2}-\left|z-z_{2}\right|^{2}=\left|z_{1}-z_{2}\right|^{2}

⇒(x−2)2+(y−3)2−(x−3)2−(y−4)2=1+1\Rightarrow(x-2)^{2}+(y-3)^{2}-(x-3)^{2}-(y-4)^{2}=1+1

⇒−4x+4+9−6y−9+6x−16+8y=2\Rightarrow-4 x+4+9-6 y-9+6 x-16+8 y=2

⇒2x+2y=14\Rightarrow 2 x+2 y=14

⇒x+y=7\Rightarrow x+y=7

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