Results 1 to 6 of 6

Math Help - locus- precalculua

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    7

    locus- precalculua

    can someone help me plz. find the locus of a point P which moves so that its distance from A(8,0) is twice its distance from the line x=2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    Let P(x,y).
    The distance from P to A is \sqrt{(x-8)^2+y^2}.
    The distance from P to the line is |x-2|.
    Now, we have
    \sqrt{(x-8)^2+y^2}=2|x-2|.
    Square both sides:
    (x-8)^2+y^2=4(x-2)^2\Rightarrow 3x^2-y^2=48
    Divide both sides by 48:
    \displaystyle \frac{x^2}{16}-\frac{y^2}{48}=1.
    So, the locus is a hyperbola.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    7
    hey thanks so much hun
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2007
    Posts
    7

    hey

    we also have to make a sketch. can u plz help me with that?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    Here's the sketch.
    Attached Thumbnails Attached Thumbnails locus- precalculua-hiperbola.jpg  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2007
    Posts
    7

    hey

    i don't understand how u got the answer for the question. can u break down the steps plz
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Locus
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 5th 2010, 10:54 PM
  2. Locus
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 20th 2010, 07:13 AM
  3. Locus
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 20th 2010, 10:57 AM
  4. locus help
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 24th 2008, 07:43 PM
  5. locus
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 14th 2008, 02:28 AM

Search Tags


/mathhelpforum @mathhelpforum