Results 1 to 4 of 4

Math Help - Circles with radius 0?

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    104

    Circles with radius 0?

    What does the equation x^2+y^2=0 represent?

    Is it a circle of radius 0? I don't think it is because that really doesn't make sense. Wouldn't it just be the degenerate conic of a point? (i.e. the point (0,0))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294

    Re: Circles with radius 0?

    Quote Originally Posted by twittytwitter View Post
    What does the equation x^2+y^2=0 represent?

    Is it a circle of radius 0? I don't think it is because that really doesn't make sense. Wouldn't it just be the degenerate conic of a point? (i.e. the point (0,0))
    Yes it's just the point (0, 0).

    There are a few ways you can think about it. I would probably do this...

    \displaystyle \begin{align*} x^2 + y^2 &= 0 \\ y^2 &= -x^2 \end{align*}

    The LHS is nonnegative, the RHS is nonpositive. So that means the only way for the equation to be satisfied is for both sides to be equal to 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,417
    Thanks
    1329

    Re: Circles with radius 0?

    But it is, strictly speaking, incorrect to talk about a "circle with radius 0". It is perfectly valid to call it a "degenerate conic section".
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294

    Re: Circles with radius 0?

    Quote Originally Posted by HallsofIvy View Post
    But it is, strictly speaking, incorrect to talk about a "circle with radius 0". It is perfectly valid to call it a "degenerate conic section".
    Why not a "degenerate circle"?
    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. Replies: 0
    Last Post: May 3rd 2011, 05:21 AM
  3. circles and radius and center
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 23rd 2010, 02:23 PM
  4. Replies: 11
    Last Post: October 12th 2009, 04:47 PM
  5. Replies: 1
    Last Post: May 28th 2009, 11:10 AM

Search Tags


/mathhelpforum @mathhelpforum