SOLUTION: Please help me with this. Find the equation of the line parallel to the line 4x+3y=24 at a distance 2 units from the origin. (note: there are two possible answers).

Algebra ->  Points-lines-and-rays -> SOLUTION: Please help me with this. Find the equation of the line parallel to the line 4x+3y=24 at a distance 2 units from the origin. (note: there are two possible answers).      Log On


   

Question 967413: Please help me with this. Find the equation of the line parallel to the line 4x+3y=24 at a distance 2 units from the origin. (note: there are two possible answers).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Find the line which contains (0,0) and has slope 3%2F4.
y-0=%283%2F4%29%28x-0%29
y=%283%2F4%29x
The general point (x,(3/4)x ).

You want to find the point on that line which is 2 units from (0,0).
sqrt%28%28x-0%29%5E2%2B%28%283%2F4%29x-0%29%5E2%29=2
sqrt%28x%5E2%2B9x%5E2%2F4%29=2
x%2Asqrt%281%2B9%2F4%29=2
x%2Asqrt%2813%2F4%29=2
%28x%2F2%29sqrt%2813%29=2
x=4%2Fsqrt%2813%29
-
Corresponding y value is (3/4)(4/sqrt(13))
y=3%2Fsqrt%2813%29.

That will be part of one possible answer.

You are looking for a line with that point just found with the equation member of 4x%2B3y because you are looking for the line PARALLEL to the given line.

highlight%284x%2B3y=4%28%284%2Fsqrt%2813%29%29%29%2B3%28%283%2Fsqrt%2813%29%29%29%29.
That needs to be simplified in order to be completely finished.