The combined equation of the pair of lines passing through the origin and making an angle 4 with the line 3x + y - 6 = 0 is...

Step-by-step solution

Slope of the given line 3x + y - 6 = 0 is m₁ = -3 . Let m be the slope of the required line. Since the angle between the lines is 4 , we have: ( 4 ) = | m - m₁ 1 + m m₁ | 1 = | m - (-3) 1 + m(-3) | = | m + 3 1 - 3m | This gives two cases: m + 3 1 - 3m = 1 m + 3 = 1 - 3m 4m = -2 m = - 1 2 m + 3 1 - 3m = -1 m + 3 = -1 + 3m 2m = 4 m = 2 The equations of the lines passing through the origin with these slopes are y = - 1 2 x and y = 2x , which can be written as x + 2y = 0 and 2x - y = 0 . The combined equation of the pa