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    Stuck on this one:

    a parabola has a cartesian equation y^2=24x

    a tangent y=mx+c is called P. show that mc is a constant, finding its value.

    I haven't a clue, i've worked out a = 6. (in the 4ax thing) but that's all i've got.

    Any suggestions?
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    (Original post by Discutimos)
    Stuck on this one:

    a parabola has a cartesian equation y^2=24x

    a tangent y=mx+c is called P. show that mc is a constant, finding its value.

    I haven't a clue, i've worked out a = 6. (in the 4ax thing) but that's all i've got.

    Any suggestions?
    this is a bit tough for the current FP1 in EDEX

    is this homework?
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    (Original post by TeeEm)
    this is a bit tough for the current FP1 in EDEX

    is this homework?
    This is AQA and it is a past paper question from 2003, according to the textbook.
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    (Original post by Discutimos)
    This is AQA and it is a past paper question from 2003, according to the textbook.
    I will run you through it

    solve simultaneously
    get expression in m, c and x
    arrange as a quadratic in x
    discriminant =0 (Tangent)
    simplifies very nicely
    this would give mc = .... number, i.e a constant
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    (Original post by TeeEm)
    I will run you through it

    solve simultaneously
    get expression in m, c and x
    arrange as a quadratic in x
    discriminant =0 (Tangent)
    simplifies very nicely
    this would give mc = .... number, i.e a constant
    Tried the first bit XD

    24x=m^2x^2 + 2mxc + c^2

    Do you compare coefficents so 2mc=24?
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    (Original post by Discutimos)
    Tried the first bit XD

    24x=m^2x^2 + 2mxc + c^2

    Do you compare coefficents so 2mc=24?
    arrange as a quadratic in x
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    (Original post by TeeEm)
    arrange as a quadratic in x
    m^2x^2 + 2mcx - 24x + c^2 = 0
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    (Original post by Discutimos)
    m^2x^2 + 2mcx - 24x + c^2 = 0
    write the coefficient of x sensibly before you consider the discrminant
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    (Original post by TeeEm)
    write the coefficient of x sensibly before you consider the discrminant

    well, it's either going to be 2mc-24 or mc-12
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    (Original post by Discutimos)
    well, it's either going to be 2mc-24 or mc-12
    The first one
    (the second one is not correct)
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    (Original post by TeeEm)
    The first one
    (the second one is not correct)

    Ok good cause i thought it was the first then you said sensibly and i got worried XD.

    I got it now, i see the discriminant simplifies to 576 = 96mc, 576/96=mc=6

    I doubted what i was doing too early on, all that csqred and msqred stuff threw me off completely, thanks for your help!
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    (Original post by Discutimos)
    Ok good cause i thought it was the first then you said sensibly and i got worried XD.

    I got it now, i see the discriminant simplifies to 576 = 96mc, 576/96=mc=6

    I doubted what i was doing too early on, all that csqred and msqred stuff threw me off completely, thanks for your help!
    all correct
    this is a standard result for parabolas...
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    (Original post by TeeEm)
    this is a standard result for parabolas...
    What do you mean?
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    (Original post by Discutimos)
    What do you mean?
    always true for a tangent on a parabola of the form y2 =4ax
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    (Original post by TeeEm)
    always true for a tangent on a parabola of the form y2 =4ax
    What as in this is a fullproof method? im not sure what you are saying is always true
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    (Original post by Discutimos)
    What as in this is a fullproof method? im not sure what you are saying is always true
    do not worry ...

    It is of no importance to your question
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    (Original post by TeeEm)
    do not worry ...

    It is of no importance to your question
    Well alrighty then XD, thanks again!
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    (Original post by Discutimos)
    Well alrighty then XD, thanks again!
    no worries
 
 
 
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