Results 1 to 4 of 4

Math Help - locus, need confirmation

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    204

    locus, need confirmation

    Q&A
    Attached Thumbnails Attached Thumbnails locus, need confirmation-locus.jpg   locus, need confirmation-locus-ans.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
    Your initial formula was correct, however, you made a few mistakes in the working.

     4 PA^2 = PB

     4 [ (y-1)^2 + (x-0)^2] = (y+2)^2 + (x-0)^2

     4y^2 - 8y + 4 + 4x^2 (you forgot to multiply 4 to x) =  y^2 + 4y + x^2

     4y^2 - y^2 -8y - 4y (you added the 4y, instead of subtracting)  + 4 -4 + 4x^2 - x^2 = 0

     3y^2 + 3x^2 -12y = 0

    Divide everything by 3 to get the answer required

    Part B is relatively straight forward. Substitute point Q into the equation of the locus and check if equality holds (it should)
    Then simply find the gradient between two points you already know (B and Q) and then use the point gradient formula.
    Last edited by Gusbob; February 2nd 2009 at 07:51 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,717
    Thanks
    634
    Hello, nikk!

    Given: points A(0,1)\text{ and }B(0,-2).
    Point P(x,y) moves such that the ratio of . PA:PB \,=\,1:2

    (a) Show that the equation of locus P is: . x^2+y^2-4y \:=\:0
    You didn't "carry the 4."

    2\cdot PA \:=\:PB \quad\Rightarrow\quad 2\sqrt{(y-1)^2 + x^2} \;=\;\sqrt{(y+2)^2+x^2}

    . . 4{\color{red}(}y^2-2y+1+x^2{\color{red})} \;=\;y^2+4y + 4 + x^2

    . . . 4y^2 - 8y + 4 + 4x^2 \;=\;y^2 + 4y + 4 + x^2

    . . . . 3x^2 + 3y^2 - 12y \;=\;0

    . . . . . . x^2 + y^2 - 4y \;=\;0




    (b) Show that point Q(2,2) is a point of the locus P.
    Substitute (2,2) into: x^2+y^2-4y \:=\:0

    . . 2^2 + 2^2 - 4(2) \;=\;0 \quad\hdots \text{ True!}




    (c) Find the equation of straiggt line BQ.
    The slope of BQ is: .  m \:=\:\frac{2-(-2)}{2-0} \:=\:2

    The equation of the line through B(0,\text{-}2) with slope m = 2 is:

    . . y - (\text{-}2) \:=\:2(x-0) \quad\Rightarrow\quad y \:=\:2x-4

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2008
    Posts
    204

    Tq

    Gusbob & Soroban tq for your help and kindness
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Just need confirmation
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 6th 2011, 10:00 PM
  2. confirmation?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 28th 2009, 05:40 PM
  3. Replies: 5
    Last Post: August 11th 2009, 06:37 AM
  4. Confirmation needed .
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 23rd 2009, 07:02 AM
  5. confirmation in regards to this question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 4th 2008, 02:44 PM

Search Tags


/mathhelpforum @mathhelpforum