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    the question is:

    find the length of the cord formed when the line x-2y+4=0 intersects the circle (x-2)^2 + (y+7)^2= 85, giving your answer in the form k*root*5 where k is a constant.

    ok so what i did was use the simultaneous method i multipplied all the brackets out without for the cirlce equation and got:

    x^2-4x+4+y^2+14y+49=85

    then for the line i rearranged it to get x=2y-4, i then sub. this into the expanded equation and got

    4y^2-16y+6-8y-16+y^2+14y+49=85

    simplifying it cleaning everything up i got:

    5y^2-10y-36=0

    now im like....i have no idea what to do:shifty: , any help would be greatly appreciated. thanks guys!
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    Firstly, there are 4 mistakes with that post:

    1) Use LaTex- (it's easier)
    2) You have spelt chord incorrectly, it's "chord" not "cord"
    3) it's not "sub"- it's substituted
    4) Plus numerous more spelling errors

    Right, firstly the chord will intercept a circle graph- like obviously. I can't be bothered to tell you the method (etc). Oh, and learn how to spell.
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    Firstly, there are 4 mistakes with that post:

    1) Use LaTex- (it's easier)
    2) You have spelt chord incorrectly, it's "chord" not "cord"
    3) it's not "sub"- it's substituted
    4) Plus numerous more spelling errors

    Right, firstly the chord will intercept a circle graph- like obviously. I can't be bothered to tell you the method (etc). Oh, and learn how to spell.
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    I'm now going to give you some help instead of being an arrogant fool who does not even realize that the TSR capitalization of LaTeX is wrong yet still copies it like a fool. Also lols because she posted twice like a fool.
    Do not listen to her, she obviously has nothing worth saying. (and is a fool)

    I would check your final equation because I believe it is wrong :p:. You have made some mistakes when substituting the line into the circle. Corrections in red
    (Original post by hopes)
    4y^2-16y+16-8y+16+4+y^2+14y+49=85

    Once you have the correct equation in y solve it and you will have found the y coordinates where they line and circle intersect. You can substitute these two value into the equation for the line to get the x values.

    Now that you have two points all you have to do is find the distance between them.

    Just post if you need any more help.
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    I'm not a fool- lol, well I maybe

    Oh and I don't get your joke- "what did the mathematician say after christmas dinner"- maybe I'm pronouncing it wrong- like a fool

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    (Original post by Sophie Maywood)
    Firstly, there are 4 mistakes with that post:

    1) Use LaTex- (it's easier)
    2) You have spelt chord incorrectly, it's "chord" not "cord"
    3) it's not "sub"- it's substituted
    4) Plus numerous more spelling errors

    Right, firstly the chord will intercept a circle graph- like obviously. I can't be bothered to tell you the method (etc). Oh, and learn how to spell.
    guy below is right, you really are a fool....fool.
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    (Original post by The Muon)
    I'm now going to give you some help instead of being an arrogant fool who does not even realize that the TSR capitalization of LaTeX is wrong yet still copies it like a fool. Also lols because she posted twice like a fool.
    Do not listen to her, she obviously has nothing worth saying. (and is a fool)

    I would check your final equation because I believe it is wrong :p:. You have made some mistakes when substituting the line into the circle. Corrections in red



    Once you have the correct equation in y solve it and you will have found the y coordinates where they line and circle intersect. You can substitute these two value into the equation for the line to get the x values.

    Now that you have two points all you have to do is find the distance between them.

    Just post if you need any more help.

    thanks alot so 5y^2-10y= 0

    factorising it gives 5y(y-2) so y= 2 so the constant k is 2 meaning its 2root5 , well thats the answer in the book anyway lol.
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    You have circles in C1? What exam board?
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    In the spoilers are a range of steps on how you would solve the question. I recommend you only use them to check what your doing/ have done and not to just copy as this will not benefit your learning.

    Spoiler:
    Show
    5y^2-10y=0

    5y(y-2)=0

    y must equal 2 or 0


    Spoiler:
    Show
    If y=0 then  x=2(0)-4=-4

    If y=2 then x=2(2)-4=0

    The coordinates of the two points of intersection are (-4,0) and  (0,2)


    Spoiler:
    Show
    The distance between two points is \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

    Distance  = \sqrt{(2-0)^2+(0-(-4))^2}= \sqrt{4+16}=\sqrt{20}=\sqrt{4\ti  mes5}=\sqrt{4} \times \sqrt{5}=2\sqrt{5}
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    (Original post by Draconis)
    You have circles in C1? What exam board?
    I do AQA which have them. Its really just added on to the geometry chapter.
 
 
 
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