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AP EAMCET202418 May 2024Morning ShiftMathematicsComplex NumberActual

The set of all real values of c for which equation z z +(4-3 i) z +(4+3 i) z+c=0 represents a circle is

Options

  1. A[25, )
  2. B[-5,5]
  3. C(- ,-5] [5, )
  4. D(- , 25]

Correct answer

D. (- , 25]

Step-by-step solution

Since, z z +(4-3 i) z +(4+3 i) z+c=0 represents a circle. Now, general equation of circle is z z +a z + a z+b=0 where, centre =-a and radius = |a|^2-b So, centre of given circle =-4+3 i aligned & and radius = |-4+3 i|^2-C = 5^2-C = 25-C & For existence of circle, radius 0 25-C 0 & 25-C 0 25 C C=(- , 25] aligned

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