Question

find the set of values ok k for which the equation zž+(-3+4i)ž-(3+4i)z+k=0 represents a circle​

Answer 1

Given : zž+(-3+4i)ž-(3+4i)z+k=0 represents a circle​

To find : set of values ok k for which the equation  represents a circle​

Solution:

zž+(-3+4i)ž-(3+4i)z+k=0

=> zž+(-3+4i)ž +(-3-4i)z+k=0

Comparing with Equation of circle

zž  + αž + α'z  + k = 0

α = -3+4i

α' = - 3 -4i

Radius of Circle  = √ |α|² - k

|α|² = (-3)² + 4²  = 25

=> Radius of Circle  =  √ (25 - k )

Radius of Circle   > 0

=> √ (25 - k ) > 0

=> 25 - k > 0

=> - k > - 25

=> k < 25

k = (-∞ , 25 )

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