AP EAMCET · Maths · Complex Number
The set of all real values of \(c\) for which equation \(z \bar{z}+(4-3 i) \bar{z}+(4+3 i) z+c=0\) represents a circle is
- A \([25, \infty)\)
- B \([-5,5]\)
- C \((-\infty,-5] \cup[5, \infty)\)
- D \((-\infty, 25]\)
Answer & Solution
Correct Answer
(D) \((-\infty, 25]\)
Step-by-step Solution
Detailed explanation
Since, \(z \bar{z}+(4-3 i) \bar{z}+(4+3 i) z+c=0\) represents a circle. Now, general equation of circle is \(z \bar{z}+a \bar{z}+\bar{a} z+b=0\) where, centre \(=-a\) and radius \(=\sqrt{|a|^2-b}\) So, centre of given circle \(=-4+3 i\)…
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