1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about circle chord midpt locus

  1. Jan 10, 2013 #1
    1. The problem statement, all variables and given/known data

    A is the pt where the circle with wquation x^2+y^2=25 cuts the positive x-axis. Find the midpts of the chords of this circle that contain the pt A

    2. Relevant equations



    3. The attempt at a solution

    Since it is about the midpt of chords, I try to set up a equation for the chords:

    y/x-5 = (√(25 - a^2)) / ((√(25 - b^2) - 5)

    where (a,b) are the pt on the circle and their ranges are -5<=a<=5 -5<=b<=5 and (x,y) are the pt will fit in the chord

    Then I used another equation which is perpendicular to the chord and pass through the center of the cirlce (0,0):

    y/x = (5 - (√(25 - b^2)) / (√(25 - a^2))

    Since the intersection of these two pts will be the mid pt of the chord by combining them together it should get the locus. But turn out to be very wired and wrong.... Please help me out!

    Thx in advance!!
     
  2. jcsd
  3. Jan 10, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can represent a point on the circle as (t,sqrt(25-t^2)). The point A is (5,0). You can find the midpoint of that chord without any line equations. Just take the sum and divide by 2.
     
    Last edited: Jan 10, 2013
  4. Jan 10, 2013 #3
    This problem is simpler if you abandon coordinates and recognize it as a homothetic transformation with center A and scale factor of 1/2. Do you know what similar figures are in Euclidean geometry? Even if you want to express your final answer in terms of an equation it will be simpler to visualize the answer and then write down the equation than it would be to derive the equation algebraically. (though I grant that your instructor might prefer the algebraic method).

    http://en.wikipedia.org/wiki/Homothetic_transformation
     
  5. Jan 10, 2013 #4
    Man can't believe the answer is so simple.... Anyway thx a lot!!!! And homothetic transformation never heard of it! Thx for letting me know! I will keep reading. But yeah I think I will just answer with the algebraic method first. Thx again for the replies!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about circle chord midpt locus
  1. Circle locus (Replies: 4)

  2. Question about circle (Replies: 16)

  3. Circles and Chords (Replies: 6)

  4. Circle theorem-Chord (Replies: 10)

Loading...