Circle And System Of Circles Question 345
Question: The length of the common chord of the circles $ x^{2}+y^{2}+2x+3y+1=0 $ and $ x^{2}+y^{2}+4x+3y+2=0 $ is
[MP PET 2000]
Options:
A) $ 9/2 $
B) $ 2\sqrt{2} $
C) $ 3\sqrt{2} $
D) $ 3/2 $
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of common chord PQ is $ 2x+1=0 $
$ C_1M $ = perpendicular distance of common chord from centre $ C_1 $
$ =| \frac{-2+1}{\sqrt{2^{2}}} |=| -\frac{1}{2} | $ Here; $ C_1,( -1,-\frac{3}{2} ),, $
$ r_1=\frac{3}{2}=C_1P $ PQ = 2PM $ =2\sqrt{C_1P^{2}-C_1M^{2}} $
$ =2\sqrt{\frac{9}{4}-\frac{1}{4}}=2\sqrt{2} $ .
BETA
