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    A line, l,has equation y=mx and a circle,C, has equation x2+ y -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 values of m, given that l and C do not intersect.

    please leave working out

    many thanks,

    keefe
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    (Original post by Kexfe)
    A line, l,has equation y=mx and a circle,C, has equation x2+ y -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 values of m, given that l and C do not intersect.

    please leave working out

    many thanks,

    keefe
    Have you managed to get started on this? What have you tried so far?
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    Here you go:

    The discriminant inequality signs in parts b) and c) should be swapped.
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    (Original post by Kexfe)
    A line, l,has equation y=mx and a circle,C, has equation x2+ y -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 values of m, given that l and C do not intersect.

    please leave working out

    many thanks,

    keefe
    (Original post by SH0405)
    Here you go:
    Make sure you understand my working, rather than just writing it down.
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    (Original post by SH0405)
    Make sure you understand my working, rather than just writing it down.
    Are you aware of the rules regarding not posting full solutions in this forum?
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    (Original post by davros)
    Are you aware of the rules regarding not posting full solutions in this forum?
    Nope.

    If I were, I wouldn't have posted a full solution.

    Sorry.
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    (Original post by SH0405)
    Nope.

    If I were, I wouldn't have posted a full solution.

    Sorry.
    Could you please delete your posts showing full solutions .. Thanks


    Also .... For your own benefit .... You parts b and c are the wrong way round
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    (Original post by TenOfThem)
    Could you please delete your posts showing full solutions .. Thanks


    Also .... For your own benefit .... You parts b and c are the wrong way round
    Are they? I don't think so.
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    Lovely handwriting
    (Original post by SH0405)
    Here you go:
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    (Original post by naxiv)
    Lovely handwriting
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    (Original post by SH0405)
    Are they? I don't think so.
    Yes

    I take it you will not be removing your solutions
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    (Original post by TenOfThem)
    Yes

    I take it you will not be removing your solutions
    Could you explain first? Pleeeaassseeee?
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    (Original post by SH0405)
    Could you explain first? Pleeeaassseeee?
    Explain what

    b^2-4ac >0 gives 2 solutions
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    (Original post by SH0405)
    ...
    Really lovely handwriting.
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    (Original post by TenOfThem)
    Explain what

    b^2-4ac >0 gives 2 solutions
    I didn't write that. There's an inequality sign error later on, but I'm pretty sure the parts and answers are fine.

    Edit. Ah, good. My answers were correct.
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    (Original post by SH0405)
    I didn't write that. There's an inequality sign error later on, but I'm pretty sure the parts and answers are fine.
    I know that you didn't write that

    Hence your error
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    (Original post by naxiv)
    Lovely handwriting
    (Original post by MathMeister)
    Really lovely handwriting.
    Really? Everyone at school keeps saying that, but I didn't think it was that great. :/
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    (Original post by TenOfThem)
    I know that you didn't write that

    Hence your error
    My answers were (thankfully) still correct though.
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    (Original post by SH0405)
    My answers were (thankfully) still correct though.
    No

    They are wrong
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    (Original post by TenOfThem)
    No

    They are wrong
    No they're not. I know I wrote down the wrong signs, but in the lines where I go from the discriminant inequalities I jump a few stages in my head. I didn't know at the time that I had got the inequality signs wrong remember. So my final answers are correct.

    The stage that I did in my head could, admittedly, have done with some written workings (well, in one sense), but it all boils down to reversing an inequality sign when one divides through by a negative. I've checked it graphically too. And after one has completed part a), it's not hard to logically deduce the answers to parts b) and c), which is why my written workings suffered, but not ​my answers.
 
 
 
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