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 `alpha` with x-axis such that `sinalpha=1/3dot`

Explanation

Given: `p = 2, sin alpha = 1/3`

`cos alpha = sqrt(1 – sin^2 alpha) = sqrt(1 – 1/9) = (2√2)/3`

The equation of the line in normal form is given by,` x cos alpha + y sin alpha = p`

Now, substitute the values, we get `x(2sqrt2)/3 + y/3 = 2 `

`(2xsqrt2+ y)/3 = 2 `


=`2sqrt2x + y = 6 `

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