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Byju's Answer
Standard XII
Mathematics
Distance Formula
Two lines pas...
Question
Two lines passing through the point
(
2
,
3
)
intersects each other at an angle of
60
∘
. If slope of one line is
2
, find equation of the other line.
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Solution
tan
θ
=
m
1
−
m
2
1
+
m
1
m
2
⇒
√
3
=
|
2
−
m
|
1
+
2
m
⇒
√
3
+
2
√
3
m
=
12
−
m
l
⇒
(
2
√
3
+
1
)
m
=
2
−
√
3
or
(
2
√
3
−
1
)
m
=
2
+
√
3
⇒
m
=
2
−
√
3
2
√
3
+
1
or
2
+
√
3
2
√
3
−
1
equation of line
=
(
y
−
3
)
=
2
±
√
3
2
√
3
∓
1
(
x
−
2
)
;
⇒
(
2
√
3
∓
1
)
(
y
−
3
)
=
(
2
±
√
3
)
(
x
−
2
)
⇒
2
√
3
y
−
y
−
6
√
3
+
3
=
2
x
−
4
+
√
3
x
−
2
√
3
or
2
√
3
y
−
6
√
3
+
y
−
3
=
2
x
−
4
−
√
3
x
+
2
√
3
⇒
(
2
√
3
−
1
)
−
(
√
3
+
2
)
x
=
−
7
+
4
√
3
or
(
2
√
3
+
1
)
y
+
(
√
3
−
2
)
x
=
−
1
+
8
√
3
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1
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