Circle And System Of Circles Question 319
Question: If the circle $ x^{2}+y^{2}=a^{2} $ cuts off a chord of length 2b from the line $ y=mx+c $ , then
Options:
A) $ (1-m^{2})(a^{2}+b^{2})=c^{2} $
B) $ (1+m^{2})(a^{2}-b^{2})=c^{2} $
C) $ (1-m^{2})(a^{2}-b^{2})=c^{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We know $ CD=| \frac{c}{\sqrt{1+m^{2}}} | $ ………….(i) But according to figure, $ a^{2}-b^{2}=CD^{2} $ From (i) and (ii), we get $ a^{2}-b^{2}=\frac{c^{2}}{(1+m^{2})} $
$ \Rightarrow (a^{2}-b^{2})(1+m^{2})=c^{2} $ .
BETA
