Circle And System Of Circles Question 30
Question: The equation of tangent to the circle $ x^{2}+y^{2}=a^{2} $ parallel to $ y=mx+c $ is
[RPET 2001]
Options:
A) 2
B) 1
C) 4
D) 3
Show Answer
Answer:
Correct Answer: D
Solution:
The centres and radii of the circles are
Centres: $ C_1( \frac{1}{2},\ 0 ),\ C_2( -\frac{1}{2},\ 0 ) $
Radii: $ r_1=\frac{1}{2},\ r_2=\frac{1}{2} $
Clearly, $ C_1C_2=r_1+r_2 $ . Therefore the circles touch each other externally.
Hence there are 3 common tangents.
BETA
