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    Im stuck again

    A line L has the equation y=mx and a circle C has equation x²+y²-6x-4y+9=0

    a) Given that L is a tangent to C find the possible values of m
    b) Find the range of values of m given that L intersects C in two distinct points
    c) Find the range of the valuse of m given that L and C do not intersect.

    :confused:
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    A line L has the equation y = mx and a circle C has equation x²+y²-6x-4y+9 = 0

    a) Given that L is a tangent to C find the possible values of m
    a) y = mx, dy/dx = m

    So differentiate, x²+y²-6x-4y+9 = 0
    re-arrange differential to make dy/dx subject. Let dy/dx = m and solve by letting y = mx in differential.
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    I must be missing something here because none of those questions make any sense. In all of those 3 situations, m could be anything. Have you not been given any coordinates of where it is a tangent to the circle or anything?
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    (Original post by Joe_87)
    I must be missing something here because none of those questions make any sense. In all of those 3 situations, m could be anything. Have you not been given any coordinates of where it is a tangent to the circle or anything?
    I think by saying the line is y=mx the line must past through the origin?... :confused: ...don't know if that helps or not...
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    (Original post by super_baros)
    I think by saying the line is y=mx the line must past through the origin?... :confused: ...don't know if that helps or not...
    Oh yeah, makes sense now, lol. I read things too quickly and obviously just read it as y = mx + c.
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    Rearrange the equation in the form (x-a)²+(y-b)²=r²
    to get...
    (x-3)²+(y-2)²=4

    then if you draw it out.... you that there is a tangent at (1,2) that also crosses the origin.... I think....so just use y2-y1/x2-x1 to find that gradient...

    Point 1 - (0,0)
    Point 2 - (1,2)
    Gradient = 2
    The other value of m is 0 as the circle touches the x axis...

    Where the line will intersect at two points will be 0<m<2

    And where it won't intersect at all will be m>2 and m<0....

    I think it's right.... somebody should check if i'm right... :p:
 
 
 
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Updated: January 26, 2006

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