Complex Numbers And Quadratic Equations question 337
Question: For all complex numbers $ z_1,z_2 $ satisfying $ |z_1|=12 $ $ \text{and }|z_2-3-4i|=5, $ the minimum value of $ |z_1-z_2| $ is [IIT Screening 2002]
Options:
A) 0
B) 2
C) 7
D) 17
Show Answer
Answer:
Correct Answer: B
Solution:
The two circles are $ C_1(0,0),r_1=12 $ , $ C_2(3,4),r_2=5 $ and it passes through origin, the centre of $ C_1 $ . $ C_1C_2=5<r_1-r_2=7 $ Hence circle $ C_2 $ lies inside circle $ C_1 $ . Therefore minimum distance between them is $ AB=C_1B-C_1A=r_1-2r_2=12-10=2. $
BETA
