if Z1=8+4i, Z2=6+4i and Z be a complex numbers such that Arg Z−Z1Z−Z2=π4 then the Locus of Z is

argx+iy−8+4ix+iy−6+4i=π4⇒x−8x−6+y−4y−4=x−6y−4−x−8y−4⇒x−72+y−52=2

if Z1=8+4i, Z2=6+4i and Z be a complex numbers such that Arg Z−Z1Z−Z2=π4 then the Locus of Z is

argx+iy−8+4ix+iy−6+4i=π4⇒x−8x−6+y−4y−4=x−6y−4−x−8y−4⇒x−72+y−52=2

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if $Z_{1} = 8 + 4 i, Z_{2} = 6 + 4 i$ and Z be a complex numbers such that $A r g (\frac{Z - Z_{1}}{Z - Z_{2}}) = \frac{π}{4}$ then the Locus of $Z$ is

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${(x - 7)}^{2} + {(y + 5)}^{2} = 2$

${(x + 7)}^{2} + {(y + 5)}^{2} = 4$

${(x - 7)}^{2} + {(y - 5)}^{2} = 2$

${(x - 7)}^{2} + {(y - 5)}^{2} = 4$

answer is A.

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$\begin{array}{l} \arg (\frac{x + i y - (8 + 4 i)}{x + i y - (6 + 4 i)}) = \frac{π}{4} \\ \Rightarrow (x - 8) (x - 6) + (y - 4) (y - 4) = (x - 6) (y - 4) - (x - 8) (y - 4) \\ \Rightarrow {(x - 7)}^{2} + {(y - 5)}^{2} = 2 \end{array}$

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if Z1=8+4i, Z2=6+4i and Z be a complex numbers such that Arg Z−Z1Z−Z2=π4 then the Locus of Z is

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if $Z_{1} = 8 + 4 i, Z_{2} = 6 + 4 i$ and Z be a complex numbers such that $A r g (\frac{Z - Z_{1}}{Z - Z_{2}}) = \frac{π}{4}$ then the Locus of $Z$ is