Circle And System Of Circles Question 238
Question: A line $ lx+my+n=0 $ meets the circle $ x^{2}+y^{2}=a^{2} $ at the points P and Q. The tangents drawn at the points P and Q meet at R, then the coordinates of R is
Options:
A) $ ( \frac{a^{2}l}{n},\frac{a^{2}m}{n} ) $
B) $ ( \frac{-a^{2}l}{n},\frac{-a^{2}m}{n} ) $
C) $ ( \frac{a^{2}n}{l},\frac{a^{2}n}{m} ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Suppose point be (h, k).
Equation of common chord of contact is $ hx+ky-a^{2}=0\equiv lx+my+n=0 $
or $ \frac{h}{l}=\frac{k}{m}=\frac{-a^{2}}{n} $
or $ h=\frac{-a^{2}l}{n} $ , $ k=\frac{-a^{2}m}{n} $ .
BETA
