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Math Help - Coordinate Geometry help

  1. #1
    W0lframit3
    Guest

    Smile 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
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  2. #2
    MHF Contributor red_dog's Avatar
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    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}
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