CircleHard
Question
If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45o at the major segment of the circle then value of m is
Options
A.2 ± √22
B.- 2 ± √2
C.- 1 ± √2
D.none of these
Solution
Equation of circles x2 + y2 = 1 = (1)2
⇒ x2 + y2 = (y - mx)2 ⇒ x2 = m2x2 - 2 mxy ⇒(1 - m2) + 2 mxy = 0
tan 45 =
⇒ 1 - m2 = ± 2m ⇒ m2 ⇒ 2m - 1 = 0
⇒ m =
= - 1 ± √2
⇒ x2 + y2 = (y - mx)2 ⇒ x2 = m2x2 - 2 mxy ⇒(1 - m2) + 2 mxy = 0
tan 45 =
⇒ 1 - m2 = ± 2m ⇒ m2 ⇒ 2m - 1 = 0⇒ m =
= - 1 ± √2Create a free account to view solution
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