Find the equation of the straight line on which the length of the perp

1.	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 the line in normal form is given by By using the formula, x cos α + y sin α = p Now, substitute the values, we get x2√2/3 + y/3 = 2 2√2x + y = 6 ∴ The equation of line in normal form is 2√2x + y = 6.

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 the line in normal form is given by

By using the formula,
x cos α + y sin α = p

Now, substitute the values, we get

x2√2/3 + y/3 = 2

2√2x + y = 6

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