Results 1 to 10 of 10

Math Help - Equation of the graph

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Equation of the graph

    Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27.


    anybody please
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428

    Re: Equation of the graph

    the distance from (0,3) to the vertical line x = 27 is 27 ... 1/3 of that distance is 9.

    now, what do you call the set of all points that are a distance 9 from the point (0,3) , and further ... what is its equation?


    also, contrary to what you may think, this is not advanced algebra ... in future, post a problem like this in the Precalculus forum.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    773

    Re: Equation of the graph

    Quote Originally Posted by rcs View Post
    Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27.
    My guess is that the word "graph" should be replaced by "locus." More importantly, the question seems to be about points whose distance from (0, 3) is 1/3 of their distance to x = 27, not 1/3 of the distance between (0, 3) and x = 27.

    After writing the equation, this seems to be an ellipse according to the classification of conic sections.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Equation of the graph

    Quote Originally Posted by rcs View Post
    Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27....
    \pm \sqrt{x^2+(-3+y)^2}=-9+\frac{x}{3}

    Attached Thumbnails Attached Thumbnails Equation of the graph-locus.png  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630

    Re: Equation of the graph

    Hello, rcs!

    Did you make a sketch?


    Find the equation of the graph of all points whose distances from (0, 3) are 1/3 of their distances from the line x = 27.
    Code:
          |
          |                       :
          |   (x,y)               :B
          |     o  *  *  *  *  *  o(27,y)
          |   * P                 :
         A| *                     :
     (0,3)o                       :
          |                       :
          |                       :
          |                       :
      - - + - - - - - - - - - - - + - -
          |                      27
    We have point P(x,y)

    Its distance from A(0,3) is: . PA \:=\:\sqrt{x^2 + (y-3)^2}

    Its distance from the line x = 27 is: . PB \:=\:27-x

    We are told that PA is one-third of PB.

    So we have the equation: . \sqrt{(x^2 + (y-3)^2} \:=\:\frac{1}{2}(27-x)

    Now simplify the equation and identify the graph.

    Follow Math Help Forum on Facebook and Google+

  6. #6
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: Equation of the graph

    sir where did you get the 1/2 ? when the problem states for the 1/3 ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    773

    Re: Equation of the graph

    Quote Originally Posted by rcs View Post
    sir where did you get the 1/2 ? when the problem states for the 1/3 ?
    1/2 in post #5 is a typo.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: Equation of the graph

    what do you mean typo? i dnt think there is 1/2 in there
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Re: Equation of the graph

    Typo means he typed it incorrectly = typed it wrong = typed it by error = not typed correctly = big finger typed = .....
    Follow Math Help Forum on Facebook and Google+

  10. #10
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: Equation of the graph

    Thank you MaxJasper ... you are the best
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: April 14th 2012, 07:05 AM
  2. Replies: 7
    Last Post: August 5th 2011, 01:30 PM
  3. Graph the equation-help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 23rd 2010, 01:04 PM
  4. Need help to graph an equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 28th 2010, 12:52 PM
  5. Equation Graph
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 5th 2009, 03:51 AM

Search Tags


/mathhelpforum @mathhelpforum