Complex Numbers And Quadratic Equations question 328
Question: The equation $ z\overline{z}+(2-3i)z+(2+3i)\overline{z}+4=0 $ represents a circle of radius [Kurukshetra CEE 1996]
Options:
A) 2
B) 3
C) 4
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ z=x+iy $ , therefore given equation becomes $ (x+iy)(x-iy)+(2-3i)(x+iy)+(2+3i)(x-iy)+4=0 $
Þ $ x^{2}+y^{2}+2x+3y-3ix+2iy+2x $ - $ 2iy+3ix+3y+4=0 $
Þ $ x^{2}+y^{2}+4x+6y+4=0 $ Therefore given equation represents a circle with radius Radius $ =\sqrt{2^{2}+3^{2}-4}=\sqrt{4+9-4}=\sqrt{9}=3 $ .
BETA
