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Math Help - Does anybody remember this equation?

  1. #1
    C.C
    C.C is offline
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    Does anybody remember this equation?

    It's a equation for finding all tangent lines to a circle when the point isn't on the circle itself. I think I remember that it was
    d=m(x)+b-(y)/√1+m^2


    But I can't remember if the x and y are in the correct place.

    Edit- Let me show an example. Find the equation of all tangent lines that can be drawn from the point (5,0) to the circle (x-0)^2+(y-0)^2=9.

    First I find the line equation.
    y-0=m(x-5)
    y=m(x-5)+0
    y=mx-5m+0

    Then I plug this into the equation, note I can only do this one because the center is at the origin because I still can't remember if the x or y are in the correct place but since they are both 0, it doesn't matter for me.
    3= m(0)-5m+0-(0)/√1+m^2

    9= 25m^2/1+m^2

    9+9m^2=25m^2
    0=14m^2-9

    Uhhh then I blank out here... So I guess I need help solving it and remembering the equation correctly...
    Last edited by C.C; April 28th 2009 at 06:17 PM.
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  2. #2
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    Quote Originally Posted by C.C View Post
    It's a equation for finding all tangent lines to a circle when the point isn't on the circle itself. I think I remember that it was
    d=m(x)+b-(y)/√1+m^2


    But I can't remember if the x and y are in the correct place.

    Edit- Let me show an example. Find the equation of all tangent lines that can be drawn from the point (5,0) to the circle (x-0)^2+(y-0)^2=9.

    First I find the line equation.
    y-0=m(x-5)
    y=m(x-5)+0
    y=mx-5m+0

    Then I plug this into the equation, note I can only do this one because the center is at the origin because I still can't remember if the x or y are in the correct place but since they are both 0, it doesn't matter for me.
    3= m(0)-5m+0-(0)/√1+m^2

    9= 25m^2/1+m^2

    9+9m^2=25m^2
    0=14m^2-9

    Uhhh then I blank out here... So I guess I need help solving it and remembering the equation correctly...
    I'll take over here: 9+9m^2=25m^2

    9+9m^2=25m^2~\implies~9=\bold{{\color{red}16}}m^2~  \implies~m^2=\dfrac9{16}~\implies~|m|=\dfrac34

    Seems to me a fairly nice result.
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