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Math Help - Center (h,k) and the radius r of each circle.

  1. #1
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    Question Center (h,k) and the radius r of each circle.

    OK, I tried doing part of this problem but now I am stuck.

    1a. Find the center (h,k) and the radius r of each circle.
    x^2+y^2+4x+2y-20=0


    x^2+y^2+4x+2y-20=0

    (x^2+4x)+(y^2+2y)=20

    (x^2+4x+4)+(y^2+2y+1)=20+4+1

    (x^2+4x+4)+(y^2+2y+1)=25

    Next Step, what exactly do I do now to solve this?
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  2. #2
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    Quote Originally Posted by wickwiki View Post
    OK, I tried doing part of this problem but now I am stuck.

    1a. Find the center (h,k) and the radius r of each circle.
    x^2+y^2+4x+2y-20=0


    x^2+y^2+4x+2y-20=0

    (x^2+4x)+(y^2+2y)=20

    (x^2+4x+4)+(y^2+2y+1)=20+4+1

    (x^2+4x+4)+(y^2+2y+1)=25

    Next Step, what exactly do I do now to solve this?
    You're kidding? After doing all the hard work you stumble one line from the finish!

    Factorise the perfect squares:

    (x + 2)^2 + (y + 1)^2 = 5^2

    Ta da!

    (*Ahem* .... it is ta da, right? You do know how to read off the centre and the radius from this?)
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