Circle And System Of Circles Question 276
Question: If the chord $ y=mx+1 $ of the circle $ x^{2}+y^{2}=1 $ subtends an angle of measure $ 45^{o} $ at the major segment of the circle then value of m is
[AIEEE 2002]
Options:
A) 2
B) - 2
C) - 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given circle is $ x^{2}+y^{2}=1 $
$ C(0,0) $ and radius = 1 and chord is $ y=mx+1 $
$ \cos 45^{o}=\frac{CP}{CR} $
$ CP= $ Perpendicular distance from (0,0) to chord $ y=mx+1 $
$ CP= $
$ \frac{1}{\sqrt{m^{2}+1}} $ (CR = radius = 1) $ \cos 45{}^\circ =\frac{1/\sqrt{m^{2}+1}}{1}\Rightarrow \frac{1}{\sqrt{2}}=\frac{1}{\sqrt{m^{2}+1}} $
$ m^{2}+1=2 $
therefore $ m=\pm 1. $
BETA
