A) Circle
B) Ellipse
C) Parabola
D) No real curve
Correct Answer: A
Solution :
\[\frac{|z-5i|}{|z+5i|}=12\]Þ \[\frac{{{x}^{2}}+{{(y-5)}^{2}}}{{{x}^{2}}+{{(y+5)}^{2}}}=12\] \[\Rightarrow \,\,\,{{x}^{2}}+{{y}^{2}}+25-10y\]\[=12\,[{{x}^{2}}+{{y}^{2}}+25+10y]\] \[\Rightarrow \,\,11{{x}^{2}}+11{{y}^{2}}+130y+275=0.\] Which represents the equation of a circle.
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