Results 1 to 3 of 3

Math Help - circles and radius and center

  1. #1
    Newbie
    Joined
    Feb 2008
    From
    florida
    Posts
    17

    Exclamation circles and radius and center

    Hi Have found the one of the circle formulas to be x^2+y^2-4x-10y+19=0. My problem is finding the radius and center with this equation. Can you help me with this question. Also, please show the steps to how you got your answer. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
     x^2+y^2-4x-10y+19=0

    Rearrange

     x^2-4x+y^2-10y+19=0

    Now complete the square in x and y

     (x^2-4x+4)-4+(y^2-10y+25)-25+19=0

     (x-2)^2-4+(y-5)^2-25+19=0

     (x-2)^2+(y-5)^2-29+19=0

     (x-2)^2+(y-5)^2-10=0

     (x-2)^2+(y-5)^2=10

     (x-2)^2+(y-5)^2=(\sqrt{10})^2

    Can you see the radius and centre?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by starrynight View Post
    Hi Have found the one of the circle formulas to be x^2+y^2-4x-10y+19=0. My problem is finding the radius and center with this equation. Can you help me with this question. Also, please show the steps to how you got your answer. Thanks!
    Hi starrynight,

    there are 2 general ways, one way being to find "g" and "f" by inspection from

    x^2+y^2+2gx+2fy+c=0

    then the centre is (-g,-f)

    then use g and f to find r, using r=\sqrt{g^2+f^2-c}

    2g=-4,\ g=-2,\ -g=2

    2f=-10,\ f=-5,\ -f=5

    g^2=4,\ f^2=25

    c=19

    centre is (2,5)

    r=\sqrt{4+25-19}=\sqrt{10}


    Alternatively, complete the squares for x and y, using half the coefficents
    of x and y.

    x^2-4x\color{blue}+(-2)^2\color{black}+y^2-10y\color{blue}+(-5)^2\color{black}+19\color{blue}-(-2)^2-(-5)^2=0

    x^2-4x+4+y^2-10y+25+19-4-25=0

    (x-2)^2+(y-5)^2-10=0

    (x-2)^+(y-5)^2=(\sqrt{10})^2=r^2

    centre is (2,5), radius is \sqrt{10}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: September 5th 2011, 08:19 PM
  2. Center and radius of circle.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 3rd 2009, 11:36 AM
  3. Replies: 11
    Last Post: October 12th 2009, 04:47 PM
  4. Radius and Center
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 31st 2008, 12:00 AM
  5. Center of Two Circles
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 27th 2008, 07:36 AM

Search Tags


/mathhelpforum @mathhelpforum