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Math Help - Studying for exam need help!

  1. #1
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    Studying for exam need help!

    Need help with this question from coordinate geometry:

    Write down the equation of any line through the point (-4, 2).
    Hence find the equations of the two lines through the point (-4, 2) whose perpendicular distance from the origin is 2.
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by milan View Post
    Need help with this question from coordinate geometry:

    Write down the equation of any line through the point (-4, 2).
    Hence find the equations of the two lines through the point (-4, 2) whose perpendicular distance from the origin is 2.
    Use y=mx+b where b is the y-intercept

    2=-4m+b, now the y-intercept can be 2 or -2 for the two lines...

    2=-4m+2
    m=0
    b=2

    2=-4m-2
    m=-1
    b=-2

    You have everything you need!
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  3. #3
    MHF Contributor red_dog's Avatar
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    The equation of the line with the slope m and passing through the point M_0(x_0,y_0) is
    y=y_0=m(x-x_0)
    In this case y-2=m(x+4) or mx-y+4m+2=0

    The distance from the point M_0(x_0,y_0) to the line ax+by+c=0 is
    \displaystyle d=\frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}
    In this case \displaystyle d=\frac{|4m+2|}{\sqrt{m^2+1}}=2\Rightarrow |2m+1|=\sqrt{m^2+1}
    Squaring both members and solving the quadratic we get
    \displaystyle m_1=0, \ m_2=-\frac{4}{3}
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  4. #4
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    One of our solutions is correct depending on the wording of the question.
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