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Completing the Square/Finding Center & Radius of Circle

  1. Feb 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the center and radius of the circle with the given equation:

    x^2+y^2+4y-117=0



    2. Relevant equations
    Completing the Square

    Formula of a Circle
    (x-h)^2-(y-k)^2=r^2

    3. The attempt at a solution
    All of the problems I've encountered like this involve completing the square. I haven't seen one where there is no X and coefficient (the same goes for Y). I was able to correctly calculate that the y-coordinate of this circle is -2. The x-coordinate is supposed to be 0 and the radius is 11, but I don't know the steps to get there. I have no x coefficient to complete the square with.

    Thank you!
     
  2. jcsd
  3. Feb 6, 2009 #2

    Mark44

    Staff: Mentor

    Not having an x term actually makes it easier. After all, x^2 = (x - 0)^2, right?
     
  4. Feb 6, 2009 #3

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    x^2+y^2+4y-117=0, also commonly notated as
    x2 + y2 + 4y - 117 = 0, may be rearranged to
    x2 + y(y + 4) - 117 =0,
    x2 + y(y + 4) = 117

    The expression with 'y' can represent a rectangle with "length" y+4 and "height" of y. This rectangle can be itself rearranged to show a missing square section. The process of completing the square is the arithmetic addition of this missing square piece. When you add this square piece to complete the square, you must do so to both sides of the equation. The goal is to be able to set the equation into standard form; it was originally given in general form. Standard form permits you to easily graph the circle.
     
  5. Feb 7, 2009 #4
    Yes, this makes sense. I still don't understand how the radius equals to 11 though..unless they rounded the square root of 113.
     
  6. Feb 7, 2009 #5

    Mark44

    Staff: Mentor

    No, they didn't round the square root of 113. How did you get 113?

    You have x^2 + y^2 + 4y - 117=0
    so x^2 + y^2 + 4y = 117

    What do you have to add to the left side to complete the square? You need to add the same amount to the right side.
     
  7. Feb 7, 2009 #6
    I'm sorry, I subtracted instead of added 4. Adding 4 to 117 is 121 and the square root of 121 is 11.

    Thanks for explaining this everyone. It was much simpler than I made it out to be.
     
  8. Feb 17, 2009 #7
    Find the standard form of the equation 16x^2+9y^2+64x-18y-71= 0
     
  9. Feb 17, 2009 #8

    Mark44

    Staff: Mentor

    You should start a new thread rather than highjack an existing thread.
     
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