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    In an implicit differentiation question (This is the 4th equation I'm doing these steps for but all have been just 3 terms, not 5), it asks:

    for the equation x^2 + y^2 - 2x - 4y - 4 = 0;

    i) find dy/dx by implicit differentiation
    Which I have done, and found dy/dx = (1-x)/(y-2).

    ii) by solving the equation for y, find the two functions defined by the equation.
    I'm struggling with this one, I've got as far as y^2 - 4y = - x^2 + 2x + 4 and can't work out how to get any further with this.

    The next two parts I think are doable once I know how to do ii.
    iii) find the derivative of each of the functions found in ii)
    iv) verify the results obtained in i) and iii) are in agreement

    Thanks in advance.
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    (Original post by ThatTallGuy)
    In an implicit differentiation question (This is the 4th equation I'm doing these steps for but all have been just 3 terms, not 5), it asks:

    for the equation x^2 + y^2 - 2x - 4y - 4 = 0;

    i) find dy/dx by implicit differentiation
    Which I have done, and found dy/dx = (1-x)/(y-2).

    ii) by solving the equation for y, find the two functions defined by the equation.
    I'm struggling with this one, I've got as far as y^2 - 4y = - x^2 + 2x + 4 and can't work out how to get any further with this.

    The next two parts I think are doable once I know how to do ii.
    iii) find the derivative of each of the functions found in ii)
    iv) verify the results obtained in i) and iii) are in agreement

    Thanks in advance.
    You have an equation of the form y^2-4y+c=0

    where c=x^2-2x-4.

    How can you solve an equation of this form?

    EDIT: Actually, it's probably quicker to write it as y^2-4y+4=-x^2+2x+8 and then factorise the left-hand-side.
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    Ah I didn't think about doing that, thank you! That made it much more simple!
 
 
 
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