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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
    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.
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    rewrite it in the form (x+a)²+(y+b)²+c=0
    √c is the radius
    (-a,-b) is the centre

    Draw out a little picture and it becomes clear that the two possible tangents are at (0,2) or (3,-1), as the line y=mx must pass through the origin.

    You can then work out the gradients using
    (y one - y two)/(x one - x two) - cant work out how to get subscript...

    HTH
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    (Original post by Fenchurch)
    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.
    completing the square on x²+y²-6x-4y+9=0
    is

    (x-3)² -9 + (y-2)² -4+9=0
    (x-3)²+(y-2)²=4 centre = (3,2)

    when x=0

    (-3)²+(y-2)²=4
    9+y²-4y+4=4
    y²-4y+9=0
    (y-2)² =2±√5 so 0,2±√5 is one set of co-ordinates

    (x-3)²+(y-2)²=4 when y=0

    (x-3)²+(-2)²=4
    (x-3)²=0
    (3,0) for co-ordinate 2

    not sure about the value m
 
 
 
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