the equation of a straight on which the perpendicular from the origin is l=2 units and this perpendicular makes an angle of 240 degree with the x-axis is
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Answer:
Using the formula of perpendicular distance of any point (x
0
,y
0
) from line ax+by+c=0 is
a
2
+b
2
∣ax
0
+by
0
+c∣
Length of perpendicular from origin on line
ax+by+c=0 is
∣
∣
∣
∣
∣
a
2
+b
2
a(0)+b(0)+c
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
a
2
+b
2
c
∣
∣
∣
∣
∣
=4units ⇒
a
2
+b
2
c
2
=16....(i)
Line ax+by+c=0 has slope m=tan120
2
=−
3
=−
b
a
⇒a
2
=3b
2
........(ii)
putting (ii) in (i)we get c
2
=16(4b
2
) ⟹c=±8b
Putting values of a,c in terms of b in the equation of line we get,
−
3
bx+by±8b=0⟹−
3
x+y±8=0
Step-by-step explanation:
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