Complex Numbers And Quadratic Equations question 335
Question: A circle whose radius is r and centre $ z_0 $ , then the equation of the circle is [RPET 2000]
Options:
A) $ z\bar{z}-z{{\bar{z}}_0}-\bar{z}z_0+z_0{{\bar{z}}_0}=r^{2} $
B) $ z\bar{z}+z{{\bar{z}}_0}-\bar{z}z_0+z_0{{\bar{z}}_0}=r^{2} $
C) $ z\bar{z}-z{{\bar{z}}_0}+\bar{z}z_0-z_0{{\bar{z}}_0}=r^{2} $
D) None of these
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Answer:
Correct Answer: A
Solution:
Equation of circle $ |z-z_0{{|}^{2}}=r^{2} $
$ \Rightarrow (z-z_0)(\overline{z-z_0})=r^{2} $
$ \Rightarrow (z-z_0)(\bar{z}-{{\bar{z}}_0})=r^{2} $ $ z\bar{z}-z{{\bar{z}}_0}-\bar{z}z_0+z_0{{\bar{z}}_0}=r^{2} $ .
BETA
