Question

If the angle between the lines y=x-6 and y=mx+6 be 60 degree find m.

Answer 1

Step-by-step explanation:

Given, lines are y=x-6 and y=mx+6

here, m1 = 1, m2 = m

angle between the lines is

tan α = m1 - m2 / 1 + m1m2

Given, angle = 60°

=> tan 60° = 1 - m / 1 + m

=> √3 = 1 - m / 1 + m

=> (1 + m) √3 = 1 - m

=> √3 + √3m = 1 - m

=> √3m + m = 1 - √3

=> m ( 1 + √3 ) = 1 - √3

=> m = 1 - √3 / 1 + √3

If want, you can rationalise the denominator