Circle And System Of Circles Question 72
Question: If line $ ax+by=0 $ touches $ x^{2}+y^{2}+2x+4y=0 $ and is a normal to the circle $ x^{2}+y^{2}-4x+2y-3=0 $ , then value of (a,b) will be
[AMU 2005]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ C_1=(0,,0)r_1=1 $ unit $ C_2=(2,,0)r_2=1 $ Clearly $ C_1C_2=r_1+r_2 $
$ =1+1=2 $ Thus two circles touch externally,
Hence the number of common tangents is 3.
BETA
