Circle And System Of Circles Question 278
Question: Length of the common chord of the circles $ x^{2}+y^{2}+5x+7y+9=0 $ and $ x^{2}+y^{2}+7x+5y+9=0 $ is
[Kurukshetra CEE 1996]
Options:
A) 9
B) 8
C) 7
D) 6
Show Answer
Answer:
Correct Answer: D
Solution:
Equation of common chord is $ S_1-S_2=0 $
therefore $ 2x-2y=0 $ i.e., $ x-y=0 $
$ \because $ Length of perpencicular drawn from $ C_1 $ to $ x-y=0 $ is $ \frac{1}{\sqrt{2}} $
$ \therefore $ Length of common chord $ =2\sqrt{\frac{19}{2}-\frac{1}{2}}=6 $ .
BETA
