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How do you complete the square when two variable are included?

  1. Aug 22, 2011 #1
    Show that the equation

    x^2+y^2-4x+10y+13=0

    represents a circle. Find the center and radius.

    This problem is to be turned in at the beginning of class
     
  2. jcsd
  3. Aug 22, 2011 #2
    You'll have to show us what you've attempted and where you're stuck. We don't just provide answers, since you don't learn anything that way.
     
  4. Aug 22, 2011 #3
    I know how to complete the square in a basic x^2+(1/2)x+2=0. If i could just get a hint as to how to deal with the y variable, that would help
     
  5. Aug 22, 2011 #4

    Mark44

    Staff: Mentor

    Use the same process on the y terms as you are doing on the x terms.
     
  6. Aug 22, 2011 #5
    Do you know whatthe form of the equation for a circle is?
     
  7. Aug 22, 2011 #6
    No i do not know the form
     
  8. Aug 22, 2011 #7

    Mark44

    Staff: Mentor

    Here's your equation:
    x2 + y2 - 4x + 10y + 13=0

    Group the x terms together and the y terms together.
    x2 - 4x + y2 + 10y= -13

    Complete the square in the x terms and complete the square in the y terms.

    One form for the equation of a circle is (x - a)2 + (y - b)2 = r2. This circle's center is at (a, b) and its radius is r. That's the form you're shooting for.
     
  9. Aug 22, 2011 #8
    Thank you so much for the help.
     
  10. Aug 22, 2011 #9
    I solved it and came up with (x-2)^2+(y+5)^2=16 meaning the center is at (2,-5) and the radius=4. Is this what you came up with as well?
     
  11. Aug 22, 2011 #10

    rock.freak667

    User Avatar
    Homework Helper

    That should be correct.
     
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