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sanfranciscan · Apr 27, 2008, 10:16 AM

Find the locus of the points which are 3 units away from the line 5x-12y-7=0.

galactus · Apr 27, 2008, 11:25 AM

What they are asking for is the equation of the two lines which will be 3 units from the given line.

You can use the distance formula or the formula for the distance from a point to a line.

To use the distance from a point to a line formula, just let x=0 and set it equal to 3 and solve for y.

$\frac{|Ax+By+C|}{\sqrt{A^{2}+B^{2}}}$

$\frac{|5(0)-12y-7|}{\sqrt{(5)^{2}+(-12)^{2}}}=3$

Solve for y. You will get two solutions. One for each line on either side of the given line.

Your given line has slope 5/12, so you know the other two lines will have the same slope.