Find the equation of the line which is at a distance of 3 units from the origin such that tan ∝ = 
where ∝ is the acute angle which this perpendicular makes with the positive direction of the x-axis.
To Find:The equation of the line.
Given : tan ∝ = 
and p =3 units.
Since tan ∝ = 
= 
Using Pythagoras theorem :
hyp = 
= 
= 13 units.
From the figure: cos ∝ = 
= 
and sin ∝ = 
= 
Formula used:
equation of the line: x cos ∝+y sin ∝ =p
x 
(
) +y × ( 
) = 5
Hence ,12x + 5y = 65 is the required equation of the line.
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