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Math Help - Intersection of a known line and two lines with an unknown variable in each.

  1. #1
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    Intersection of a known line and two lines with an unknown variable in each.

    I'm trying to do number 7 on page 10 of this document: http://www.edexcel.com/migrationdocu...athematics.pdf

    I have done parts a and b. The answers give x=-4 but I don't know how that is obtained.

    The method used for part b is questionable as I would use implicit differentiation. You cannot simply convert to an expression starting with y= when that type of equation isn't suitable. It is also questionable why the value of a is not used in b but that is a minor point.
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    Senior Member Paze's Avatar
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    This is in the wrong sub-forum. You should post this in the university math board.
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    It is pre-university mathematics since it is a question from A-level.
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    Senior Member Paze's Avatar
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    I thought you meant that you needed help with implicit differentiation.
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    Quote Originally Posted by Stuck Man View Post
    It is pre-university mathematics since it is a question from A-level.

    Frankly, I don't know what problem you asking about.
    All of this could have been avoided if you would just take the time to past the question.

    It is so easy to use very basic LaTeX.
    On the toolbar you will see \boxed{\Sigma} clicking on that give the LaTeX wraps, [tex] [/tex]. The code goes between them.

    Here are some examples.
    [tex]y^{2}=4ax [/tex] gives  y^2=4ax

    [tex] \frac{2x+1}{x^{2}+x+1} [/tex] gives  \frac{2x+1}{x^2+x+1}

    [tex] \sqrt{x+1} [/tex] gives  \sqrt{x+1}

    OR
    You can also click on Reply with Quote. That will allow you to ‘steal’ any code that you see that you like.
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  6. #6
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    I am trying to do part c. I have figured there is an infinite number of points on the line y=15 where x<0 that could be the point of intersection. The answers give x=-4 which is presumably the nearest point that allows t in both of the tangents to be an integer or a rational number. The question does not give enough information to solve the coordinates of A and B.
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: Intersection of a known line and two lines with an unknown variable in each.

    Hi Stuck Man!

    I'm afraid your assumption about x=-4 is incorrect.
    There is a piece of information in the problem that you have not used yet.
    It says that both tangent lines meet on the directrix of C where y=15.
    The parabola y^2=4ax has a directrix at x=-a.
    In other words, both tangents go through the point (-4,15).

    For the meaning of the word directrix, see for instance: Conic section - Wikipedia, the free encyclopedia.
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