[JEE Advanced 1990] $Z_1=10+6i,\ Z_2=4+6i$. If $\arg\dfrac{Z-Z_1}{Z-Z_2}=\dfrac\pi4$, prove that $|Z-7-9i|=3\sqrt2$.
$Z_1=10+6i,\ Z_2=4+6i$. If $\arg\dfrac{Z-Z_1}{Z-Z_2}=\dfrac\pi4$, prove that $|Z-7-9i|=3\sqrt2$.
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✓ Vidaara Team
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· 1mo ago
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Answer: Proved.
A constant argument $\frac\pi4$ between $Z-Z_1$ and $Z-Z_2$ makes $Z$ trace an arc of a circle through $Z_1,Z_2$; its centre is $7+9i$ and radius $3\sqrt2$, so $|Z-7-9i|=3\sqrt2$.
JEE Advanced 1990 · Complex Numbers — verified solution by the Vidaara Team.
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