12. 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.
Answers
Answer:
your answer is given above
Answer:
It is given that the slope of the first line m
1
=2
Let the slope of the other line be m
2
The angle between the two lines is 60
∘
∴tan60
∘
=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
⇒
3
=
∣
∣
∣
∣
∣
1+2m
2
2−m
2
∣
∣
∣
∣
∣
⇒
3
=±{
1+2m
2
2−m
2
}
⇒
3
=
1+2m
2
2−m
2
or
3
=−{
1+2m
2
2−m
2
}
⇒
3
(1+2m
2
)=2−m
2
or
3
(1+2m
2
)=−(2−m
2
)
⇒
3
+2
3
m
2
+m
2
=2or
3
+2
3m
2
−m
2
=−2
⇒m
2
=
(2
3
+1)
2−
3
orm
2
=
2
3
−1
−(2+
3
)
The equation of line passing through point (2,3) and having a slope of
2
3
+1
(2−
3
)
is
(y−3)=
2
3
+1
2−
3
(x−2)
(2
3
+1)y−3(2
3
+1)=(2−
3
)x−2(2−
3
)
(
3
−2)x+(2
3
+1)y=−1+8
3
In this case the equation of the other line is (
3
−2)x+(2
3
+1)y=−1+8
3
similarly for another one.
Step-by-step explanation:
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