# Coordinate Geometry help

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• Nov 22nd 2007, 11:26 AM
W0lframit3
Coordinate Geometry help
Hi. Ive did a few of these sums now, but I am stuck at this one:

Find the equations of the two lines which pass through the point (1,3) if the perpendicular distance of each line from the origin is 3.

I know you have to use the perp. distance formula in there somewhere, but im really stuck on the method of obtaining the answer.
Could someone please explain the method to me. Thanks
• Nov 22nd 2007, 01:14 PM
red_dog
Let $y=mx+n$ be the equation of the line.
If the line passes through the point (1,3), then $m+n=3$.
The distance from the point $(x_0,y_0)$ to the line is $\displaystyle d=\frac{|y_0-mx_0-n|}{\sqrt{m^2+1}}$.
In this case, the distance from origin to the line is $\displaystyle \frac{|n|}{\sqrt{m^2+1}}=3$.
Now, we have the system
$\left\{\begin{array}{ll}m+n=3\\3\sqrt{m^2+1}=|n|\e nd{array}\right.$.
Solving the system we get $m_1=0,n_1=3, \ m_2=-\frac{3}{4},n_2=\frac{15}{4}$