convert x+√3y=8 into normal form
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Step-by-step explanation:
The given equation is
x−
3
y+8=0
which can be written as
x−
3
y=−8
⇒−x+
3
y=8
On dividing both sides by
(−1)
2
+(
3
)
2
=
4
=2, we get
−
2
x
+
2
3
y=
2
8
⇒(−
2
1
)x+(
2
3
)y=4
⇒xcos120
∘
+ysin120
∘
=4
which is the normal form.
On comparing it with the normal form of equation of line
xcosα+ysinα=p, we get
α=120
∘
and p=4
So, the perpendicular distance of the line from the origin is 4 and the angle between the perpendicular and the positive x-axis is 120
∘
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