Trigonometric EquationHard
Question
The equation of the bisector of the acute angle between the lines 2x - y + 4 = 0 and x - 2y = 1 is :-
Options
A.x + y + 5 = 0
B.x - y + 1 = 0
C.x - y - 5 = 0
D.None of these
Solution
The equations of the lines are
2x - y + 4 = 0 and - x + 2y + 1 = 0
We have, 2 × - 1 + (-1) × 2 < 0 i.e. a1a2 + b1b2 < 0
Therefore, the equation of the bisector of acute angles is
⇒ 2x - y + 4 = - x + 2y + 1
⇒ 3x - 3y + 3 = 0
⇒ x - y + 1 = 0
2x - y + 4 = 0 and - x + 2y + 1 = 0
We have, 2 × - 1 + (-1) × 2 < 0 i.e. a1a2 + b1b2 < 0
Therefore, the equation of the bisector of acute angles is
⇒ 2x - y + 4 = - x + 2y + 1
⇒ 3x - 3y + 3 = 0
⇒ x - y + 1 = 0
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