Circle And System Of Circles Question 89
Question: If the circles $ x^{2}+y^{2}-9=0 $ and $ x^{2}+y^{2}+2ax+2y+1=0 $ touch each other, then a =
[Roorkee Qualifying 1998]
Options:
A) - 4/ 3
B) 0
C) 1
D) 4/3
Show Answer
Answer:
Correct Answer: D
Solution:
When two circles touch each other externally, then $ r_1+r_2=\sqrt{{{{ 0-(-a) }}^{2}}+{{{ 0-(-1) }}^{2}}} $
$ \Rightarrow (3+a)=\sqrt{a^{2}+1}\Rightarrow a=-4/3 $ . When two circles touch each other internally, then $ r_1-r_2=\sqrt{{{{ 0-(-a) }}^{2}}+{{{ 0-(-1) }}^{2}}} $
$ \Rightarrow (3-a)=\sqrt{a^{2}+1}\Rightarrow a=4/3 $ .
BETA
