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    Name:  lolol.png
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Size:  3.3 KBHey there
    I am really lost with the question and would appreciate help

    I just don't know how to go about it and the mark scheme is not helping at all

    thanks
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    (Original post by madfish)
    Name:  lolol.png
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Size:  3.3 KBHey there
    I am really lost with the question and would appreciate help

    I just don't know how to go about it and the mark scheme is not helping at all

    thanks
    Complete the square on the LHS, and note that circles have equations of the form

    (x-a)^2 + (y-b)^2 = r^2

    where r is the radius, and (a,b) is the centre.

    Hint:

    \displaystyle x^2 - 2ax = (x-a)^2 - a^2
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    (Original post by Indeterminate)
    Complete the square on the LHS, and note that circles have equations of the form

    (x-a)^2 + (y-b)^2 = r^2

    where r is the radius, and (a,b) is the centre.

    Hint:

    \displaystyle x^2 - 2ax = (x-a)^2 - a^2
    Okay i complete the square to get :

    (x-8)^2 + (y + a/2)^2

    therefore

    45= 64 - (a/2)^2

    And it's not giving me the correct answer
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    (Original post by madfish)
    Okay i complete the square to get :

    (x-8)^2 + (y + a/2)^2

    therefore

    45= 64 - (a/2)^2

    And it's not giving me the correct answer
    Look at the final line.

    You've subtracted them both on the LHS, so they have to be positive on the RHS with the -20
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    (Original post by madfish)

    45= 64 - (a/2)^2
    You forgot about the 20 and you have a sign error.
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    (Original post by Indeterminate)
    Look at the final line.

    You've subtracted them both on the LHS, so they have to be positive on the RHS with the -20
    it is the 20 part I am confused about on the mark scheme.. why do we include it? thanks
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    (Original post by madfish)
    it is the 20 part I am confused about on the mark scheme.. why do we include it? thanks
    You have to include it because that's part of the "broken down" form of the equation that was given to you on the paper.
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    (Original post by madfish)
    it is the 20 part I am confused about on the mark scheme.. why do we include it? thanks
    When you say "why do we include it" it would be more valid to enquire why you excluded it?
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    (Original post by Indeterminate)
    You have to include it because that's part of the "broken down" form of the equation that was given to you on the paper.
    what exactly is the 20? the radius? a coordinate? a constant?
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    (Original post by madfish)
    what exactly is the 20? the radius? a coordinate? a constant?
    A constant. You don't do anything to it when you complete the square, so why exclude it?
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    (Original post by madfish)
    Okay i complete the square to get :

    (x-8)^2 + (y + a/2)^2

    therefore

    45= 64 - (a/2)^2

    And it's not giving me the correct answer
    So

    x^2-16x + y^2+ay + 20 = 0

    So

    (x-8)^2 - 64 + (y+\frac{a}{2})^2 - \frac{a^2}{4} + 20 = 0

    So

    (x-8)^2 + (y+\frac{a}{2})^2 = 44 + \frac{a^2}{4}

    And you are told that the RHS = 45
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    (Original post by Indeterminate)
    A constant. You don't do anything to it when you complete the square, so why exclude it?
    I am really confused still... surely we only need the centre coordinates and the radius to find a? ( i know now i am wrong.. but how?)
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    (Original post by madfish)
    I am really confused still... surely we only need the centre coordinates and the radius to find a? ( i know now i am wrong.. but how?)
    That is what you need

    Well, actually, as I have shown, you only need the radius
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    (Original post by madfish)
    I am really confused still... surely we only need the centre coordinates and the radius to find a? ( i know now i am wrong.. but how?)
    If I have

    (x-4)^2 + (y-8)^2  - 80 + a =0

    then

    \displaystyle r= \sqrt{80-a}

    \displaystyle r^2 = 80 - a

    by the definition of a circle.
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    Note 'R' and rearrange!

    Posted from TSR Mobile
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    (Original post by TenOfThem)
    So

    x^2-16x + y^2+ay + 20 = 0

    So

    (x-8)^2 - 64 + (y+\frac{a}{2})^2 - \frac{a^2}{4} + 20 = 0

    So

    (x-8)^2 + (y+\frac{a}{2})^2 = 44 + \frac{a^2}{4}

    And you are told that the RHS = 45
    Thanks TenOfthem

    So where do i go from here?
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    (Original post by madfish)
    Thanks TenOfthem

    So where do i go from here?
    The RHS = 45

    I am sure that you can solve

    44 + \frac{a^2}{4} = 45
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    (Original post by madfish)
    Thanks TenOfthem

    So where do i go from here?
    You know 44 + \frac{a^{2}}{4} = 45 so solve for 'a' and show you can get the required solutions
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    (Original post by TenOfThem)
    The RHS = 45

    I am sure that you can solve

    44 + \frac{a^2}{4} = 45
    hmmm haha

    yea I hopefully will be able too

    thanks tenofthem btw, nominated you for most helpful member of the month
 
 
 
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