Question

2 lines passing through the point (2,3)intersects each other at an angle of 60 degree if slope of one line is 2, find equation of other line

Answer 1

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

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