Circle And System Of Circles Question 341
Question: The line $ lx+my+n=0 $ will be a tangent to the circle $ x^{2}+y^{2}=a^{2} $ if
[MNR 1974; AMU 1981]
Options:
A) $ n^{2}(l^{2}+m^{2})=a^{2} $
B) $ a^{2}(l^{2}+m^{2})=n^{2} $
C) $ n(l+m)a $
D) $ a(l+m)=n $
Show Answer
Answer:
Correct Answer: B
Solution:
Line $ y=mx+c $ is tangent, if $ c=\pm a\sqrt{1+m^{2}} $ . Now $ lx+my+n=0 $ or $ y=-\frac{l}{m}x-\frac{n}{m} $ is tangent, if $ -\frac{n}{m}=\pm a\sqrt{1+{{( \frac{l}{m} )}^{2}}} $ or $ n^{2}=a^{2}(m^{2}+l^{2}) $ .
BETA
