Question

The two lines passing through the point (2,3) intersect each other at angle of 60 degree. If the slope of one line is 2,then find the equation of the second line

Answer 1

I think it may help you.

Answer 2

Answer:

Step-by-step explanation:

L1 :   (y - 3)/(x-2) = 2,  or    y = 2 x - 1

L2 :  (y - 3)/(x-2) = m.   ie.,  y = m x - (2m-3)  

Ф = angle between the lines = 60°.

Tan Ф = (2 - m)/[1 + 2 m]  

(2√3 + 1) m = 2 - √3

m = (2 -√3)(2√3 -1)/11 = (5√3-8)/11

Equation of the 2nd line is:  

     11 y = (5√3 - 8) x + 33 - 2(5√3 - 8)

     11 y = (5√3 - 8) x + 49 - 10 √3