specify the method to solve the below given question.( as i know the answer but not the correct method to solve it ) :

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   with the x axis such that sin  = 1 / 3     (answer : 2 2x+y = 6  )

solution:

let the equation of the line be y=mx+c,

 

since,  sin =1/3 , therefore, tan  = 1/22

=> m= -22(since the lines are perpendicular)

 

the equation now becomes y + 22x - c = 0

 

the line is at a distance of 2 units from the origin, so

using the "perpendicular distance of a point from a line" formula,

we get, | -c/3 | = 2

=>c=6

 

therefore, the final equation is y + 22x = 6

 

ask me if you didn't understand the solution.....

 

 

Its very simple. Once again use the normal form of equation of a line.Ihave given the detailed explaination of normal form in your previous post.  Now the normal form of equation of a ine is given by xcos+ysin.Hence cos=2^{[ ]}2/8 . Hence v get the final equation of  the line.