Conic Sections Question 489
Question: If the chord y=mx+1 of the circle $ x^{2}+y^{2}=1 $ subtends an angle of measure $ 45{}^\circ $ at the major segment of the circle, then the value of m is
Options:
A) $ 2\pm \sqrt{2} $
B) $ -2\pm \sqrt{2} $
C) $ -1\pm \sqrt{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] From the figure, $ OB=1,OD=\frac{1}{\sqrt{2}} $ Also, $ OD=\frac{| m(0)-0+1 |}{\sqrt{m^{2}+1}} $ So, we have $ \frac{| m(0)-0+1 |}{\sqrt{m^{2}+1}}=\frac{1}{\sqrt{2}} $
$ \therefore m=\pm 1 $
BETA
