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
0
1
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=-1 $ . 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
