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Math Help - Complete the equation?

  1. #1
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    Complete the equation?

    Complete the equation of the circle centered at that passes through

    __________=0

    I know I need to get into the form x^2+Dx+y^2+Ey+F=R^2 just not sure ?
    I am at this point (x+7)^2+(y-9)^2=r^2 I need help to expand it out
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    Re: Complete the equation?

    Quote Originally Posted by M670 View Post
    Complete the equation of the circle centered at that passes through __________=0
    I know I need to get into the form x^2+Dx+y^2+Ey+F=R^2 just not sure ? I am at this point (x+7)^2+(y-9)^2=r^2 I need help to expand it out
    YES and r^2=(-7-4)^2+(9-1)^2

    You should know the basic algebra: (x+7)^2=x^2+14x+49.
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    Re: Complete the equation?

    Hello, M670!

    \text{Find the equation of the circle centered at }C(\text{-}7,9)\text{ that passes through }P(4,1).

    You're making hard work out of it . . .

    The equation of a circle with center (h,k) and radius r is: . (x-h)^2 + (y-k)^2 \:=\:r^2

    You already know the center: . C(\text{-}7,9)

    You need only the radius . . . r \:=\:\overline{CP}
    . . Use the Distance Formula.
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    Re: Complete the equation?

    Quote Originally Posted by Plato View Post
    YES and r^2=(-7-4)^2+(9-1)^2

    You should know the basic algebra: (x+7)^2=x^2+14x+49.
    So I came up with x^2+14x+y^2-18y+130=0 but that still isn't right and I dont know why? I need to write formula =0
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    Re: Complete the equation?

    Quote Originally Posted by M670 View Post
    So I came up with x^2+14x+y^2-18y+130=0 but that still isn't right and I dont know why? I need to write formula =0
    You did not use the fact r^2=185, did you?
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    Re: Complete the equation?

    Quote Originally Posted by Plato View Post
    You did not use the fact r^2=185, did you?
    No I did not use the r^2=185 as I know the circle formula to be [tex](x-h)^2+(y-K)^2=r^2[/tex} since it's asking me for the equation equal to zero I am not sure where I would put radius?
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    Re: Complete the equation?

    Quote Originally Posted by M670 View Post
    No I did not use the r^2=185 as I know the circle formula to be [tex](x-h)^2+(y-K)^2=r^2[/tex} since it's asking me for the equation equal to zero I am not sure where I would put radius?

    I don't think any of us can help you understand this question.
    Your misunderstanding is very profound.
    Please sit down with a live tutor. Go over what this question means.
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    Re: Complete the equation?

    Quote Originally Posted by Plato View Post
    I don't think any of us can help you understand this question.
    Your misunderstanding is very profound.
    Please sit down with a live tutor. Go over what this question means.
    Thanks for trying, Its this web program called webworks, It really sucks as you have to answer it a specific way or esle it wont except it.
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    Re: Complete the equation?

    You know that the centre is \displaystyle \begin{align*} (-7, 9) \end{align*} and one point on your circle is \displaystyle \begin{align*} (4, 1) \end{align*}. The radius is the distance between the centre to any point on the circle, so how can you work out the distance between these two points?
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    Re: Complete the equation?

    Quote Originally Posted by Prove It View Post
    You know that the centre is \displaystyle \begin{align*} (-7, 9) \end{align*} and one point on your circle is \displaystyle \begin{align*} (4, 1) \end{align*}. The radius is the distance between the centre to any point on the circle, so how can you work out the distance between these two points?
    Yes I know I can use the standard distance formula which will give my radius of the circle but the question was asking me the equation of a circle with its center at (-7,9) and passes throught points (4,1)
    Last edited by M670; December 2nd 2012 at 04:00 PM.
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    Re: Complete the equation?

    Quote Originally Posted by M670 View Post
    Yes I know I can use the standard distance formula which will give my radius of the circle but the question was asking me the equation of a circle with its center at (-7,9) and passes throught points (4,1)
    Well damn it, use it!
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    Re: Complete the equation?

    I don't think you've bothered reading the posts above you. If you have the centre and radius of your circle, substitute them into this:

    \displaystyle \begin{align*} (x - h)^2 + (y -k)^2 = r^2 \end{align*}

    where \displaystyle \begin{align*} (h, k) \end{align*} is the centre of your circle and \displaystyle \begin{align*} r \end{align*} is the radius.

    This is the general form of the equation of a circle. But since you are asked to set the equation equal to 0, you expand everything and move everything to one side.
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    Re: Complete the equation?

    Ok So h=-7 k=9 r= \sqrt185 (x+7)^2+(y-9)^2=\sqrt185 which is then x^2+14x+49+y^2-18y+81=\sqrt185

    HOLY SH** it just dawned on me x^2+14x+y^2-18y-55=0 is the correct answer....
    Let's hope it doesn't take me this long on my final...
    Many thanks Prove it and Plato...
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    Re: Complete the equation?

    Actually \displaystyle \begin{align*} r = \sqrt{185} \end{align*} so \displaystyle \begin{align*} r^2 = 185 \end{align*} which means \displaystyle \begin{align*} (x + 7)^2 + (y - 9)^2 = 185 \end{align*}.
    Thanks from puresoul
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