Two lines passing through the point (2,3) intersect each other at an angle of 60° . If slope of one line is 2, find the equation of the other line.

Now, θ = 60° , m₁= 2. Now we find m₂(the slope of the other line)
We have tanθ =

Part I

tan60° =

=

+2m₂=2-m₂

m₂(2+1)=2-

Therefore equation of the other line is

y - 3 =

(y - 3)(2 + 1) = (2 -)(x - 2)

(2 - 1)y + 3(2 + 1) = (2 - )x - 2(2 - )

( - 2)x + (2 + 1)y = 6 + 3 - 4 + 2

( - 2)x + (2 + 1)y = 8 - 1.

Part II

tan 60 =

=

+ 2m₂ = m₂ - 2

m₂(2 - 1) = (-2 - )

m₂ =

Equation of the other line is

y - 3 = (x - 2)

(2-1)(y - 3) = -(2 + )(x - 2)

(2 - 1)y - 3(2 - 1) = -(2 +)x + 2(2 + )

(2 +)X + (2 - 1)Y = 4 + 2 + 6

(2 +)x + (2 - 1)y = 8 + 1 is the equation required.