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Question -

Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle α given by tan α = 5/12 with the positive direction of x–axis.



Answer -

Given:

p = 3, α = tan-1 (5/12)

So, tan α = 5/12

sin α = 5/13

cos α = 12/13

The equation of theline in normal form is given by

By using the formula,

x cos α + y sin α= p

Now, substitute thevalues, we get

12x/13 + 5y/13 = 3

12x + 5y = 39

∴ The equation of linein normal form is 12x + 5y = 39.

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