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Question -

Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x–axis such that sin α = 1/3.



Answer -

Given:

p = 2, sin α = 1/3

We know that cos α =√(1 – sin2 α)

= √(1 – 1/9)

= 2√2/3

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

x2√2/3 + y/3 = 2

2√2x + y = 6

∴ The equation of linein normal form is 2√2x + y = 6.

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