Q. 465.0( 2 Votes )
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.
Answer :
Now, θ = 60° , m1= 2. Now we find m2(the slope of the other line)
We have tanθ =

Part I
tan60° =
=
+2
m2=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 =
=
+ 2
m2 = 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.
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