"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"

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"$\left|z-z_{1}\right|^{2}-\left|z-z_{2}\right|^{2}=\left|z_{1}-z_{2}\right|^{2}$

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

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

$\Rightarrow 2 x+2 y=14$

$\Rightarrow x+y=7$"

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

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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

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