Question

Find the equation of the straight line passing through the point 1, 2 and making an angle 60° with the line root 3 x + y + 2 is equal to zero

Answer 1

Please see the attachment

Answer 2

y = 2 or  y = √3x +  2 - √3

Step-by-step explanation:

Making angle 60°  with √3x + y + 2 = 0

=> y = -√3x - 2

Slope = -√3

Let say sloe of other line = m

=> Tan 60° = |(m - (-√3)) / (1  + m(  -√3))|

=> √3 = | (m + √3) /(1 - m√3) |

squaring both sides

=> 3 = (m² + 3 + 2√3m) / (1 + 3m² - 2m√3)

=> 3 + 9m² - 6m√3 = m² + 3 + 2√3m

=> 8m² -  8m√3 = 0

=> 8m(m - √3) = 0

m = 0 or m = √3

y = c  or y = √3x + c

passed through 1 , 2

=> y = 2    or   2 = √3 + c  => c = 2 - √3

=> y = √3x +  2 - √3

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