If $z_1=10+6 i, z_2=4+6 i$ an $z$ is any complex number such that the argument of…

If $z_1=10+6 i, z_2=4+6 i$ an $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_2\right)}$ is $\frac{\pi}{4}$, then
  1. $|z-7-9 i|=3 \sqrt{2}$
  2. $|z-7-9 i|=2 \sqrt{2}$
  3. $|z-3+9 i|=3 \sqrt{2}$
  4. $|z+3-9 i|=2 \sqrt{2}$

Solution

$\operatorname{arg}\left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{4}$
Locus of $z$ lies on circle Angle subtended at centre $=\frac{\pi}{2}$ Centre of circle is $(7+9 i)$ Radius $=3 \sqrt{2}$ $|z-(7+9 i)|=3 \sqrt{2}$

Asked in: AP EAMCET 2024 (20 May Shift 2)

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