Results 1 to 2 of 2

Math Help - Stuck... beginner

  1. #1
    Newbie
    Joined
    Jun 2006
    Posts
    3

    Stuck... beginner

    Find the normal to the curve x^2 + y^2 = 2x + 2y that is parallel to the line x+y = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, yakkow!

    Find the normal to the curve x^2 + y^2 = 2x + 2y that is parallel to the line x+y = 0
    Differentiate implicitly: . 2x + 2y\cdot y' \:= \:2 + 2y' \quad\Rightarrow\quad 2y\cdot y' - 2y'\;=\;2 - 2x

    Factor: . 2(y - 1)y'\:=\:2(1 - x)\quad\Rightarrow\quad y'\:=\:\frac{1-x}{y-1} . . . slope of the tangent

    The slope of the normal is: . m\:=\:\frac{y-1}{x-1}

    The line x + y\:=\;0\quad\Rightarrow\quad y \,=\,-x has slope -1.

    So we have: . \frac{y - 1}{x - 1}\:=\:-1\quad\Rightarrow\quad y\,=\,2 - x

    Substitute into the original equation:
    . . . x^2 + (2 - x)^2\:=\:2x + 2(2 - x)\quad\Rightarrow\quad2x^2 - 4x\:= 0\quad\Rightarrow\quad x \,=\,0,\;2

    The corresponding y-values are: y\,=\,2,\;0

    We seem to have two normals: one at (2,0), another at (0,2)


    At (2,0) with slope -1, the equation of the normal is:
    . . . y - 0\:=\:-1(x - 2)\quad\Rightarrow\quad y \:=\:-x + 2

    At (0,2) with slope -1, the equation of the normal is:
    . . . y - 2\:=\:-1(x - 0)\quad\Rightarrow\quad y\:=\:-x + 2

    Ha! . . . It's the same line!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Beginner at definite integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 27th 2010, 05:33 PM
  2. integration (beginner)
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 12th 2009, 03:41 PM
  3. STATA beginner
    Posted in the Math Software Forum
    Replies: 0
    Last Post: January 4th 2009, 05:37 PM
  4. Beginner to mathematica
    Posted in the Math Software Forum
    Replies: 8
    Last Post: November 13th 2008, 01:39 PM
  5. MatLab Help for Beginner
    Posted in the Math Software Forum
    Replies: 3
    Last Post: June 22nd 2008, 07:55 PM

Search Tags


/mathhelpforum @mathhelpforum