Circle And System Of Circles Question 219
Question: The length of common chord of the circles $ x^{2}+y^{2}=12 $ and $ x^{2}+y^{2}-4x+3y-2=0 $ , is
[RPET 1990, 99]
Options:
A) $ 4\sqrt{2} $
B) $ 5\sqrt{2} $
C) $ 2\sqrt{2} $
D) $ 6\sqrt{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
The equation of common chord $ \equiv S_1-S_2=0 $ or $ 4x-3y-10=0 $ and centre of first circle is (0, 0).
Therefore perpendicular from it on line is $ p_1=\frac{10}{5}=2 $ and $ R_1=\sqrt{12} $ .
Hence $ L_1L_2=2\sqrt{(R_1^{2}-p_1^{2})}=2\sqrt{(12-4)}=4\sqrt{2} $ .
BETA
