Complex Numbers And Quadratic Equations question 375
Question: The equation $ |z-5i|\div |z+5i|=12, $ where $ z=x+iy, $ represents a/an [AMU 1999]
Options:
A) Circle
B) Ellipse
C) Parabola
D) No real curve
Show Answer
Answer:
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 11x^{2}+11y^{2}+130y+275=0. $ Which represents the equation of a circle.
BETA
