Conic Sections Question 519
Question: The line $ lx+my-n=0 $ will be tangent to the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ , if
Options:
A) $ a^{2}l^{2}+b^{2}m^{2}=n^{2} $
B) $ al^{2}+bm^{2}=n^{2} $
C) $ a^{2}l+b^{2}m=n $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\frac{-l}{m}x+\frac{n}{m} $ is tangent to $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ , if $ \frac{n}{m}=\pm \sqrt{b^{2}+a^{2}{{( \frac{l}{m} )}^{2}}} $ or $ n^{2}=m^{2}b^{2}+l^{2}a^{2} $ .
BETA
