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Byju's Answer
Standard XII
Mathematics
Pair of Lines
Find the angl...
Question
Find the angle between
√
3
x
+
y
+
16
=
0
and
√
3
x
−
y
+
9
=
0
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Solution
We have,
√
3
+
y
+
16
=
0
a
n
d
√
3
−
y
+
9
=
0
then,
√
3
+
y
+
16
=
0
−
−
−
(
1
)
√
3
−
y
+
9
=
0
−
−
−
−
(
2
)
By equation (1)
√
3
+
y
+
16
=
0
y
=
−
√
3
−
16
on compare that,
y
=
m
1
x
+
c
m
1
=
−
√
3
By equation (2),
√
3
−
y
+
9
=
0
y
=
√
3
x
+
9
on compare that,
y
=
m
2
x
+
c
m
2
=
√
3
then,
we know that
angle between
tan
θ
=
m
2
∼
m
1
1
+
m
1
m
2
tan
θ
=
√
3
−
(
−
√
3
)
1
+
(
−
√
3
)
×
√
3
tan
θ
=
2
√
3
1
+
(
√
3
)
2
tan
θ
=
2
√
3
1
+
3
tan
θ
=
2
√
3
4
tan
θ
=
√
3
2
θ
=
tan
−
1
√
3
2
Hence, this is the answer.
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