Question

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​

Answer 1

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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