Results 1 to 2 of 2

Math Help - Hyperbola exercise

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    34

    Hyperbola exercise

    can someone help me with this exercise ? So far , I only know that the first element of the equation is 5.

    If the asymptotes of the hyperbolic path of a particle are given by y = + - 3/4x and the closest the particle comes to the nucleus is 5 units , find the equation of the particle's path.

    * see attachment

    Thanks in advance!!
    Attached Thumbnails Attached Thumbnails Hyperbola exercise-img031.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,811
    Thanks
    701
    Hello, Vance!

    If the asymptotes of the hyperbolic path of a particle are given by y = \pm\tfrac{3}{4}x
    and the closest the particle comes to the nucleus (origin) is 5 units,
    find the equation of the particle's path.

    From the asymptotes, we have: . \frac{b}{a} \:=\:\frac{3}{4} \quad\Rightarrow\quad b \:=\:\tfrac{3}{4}a

    Since a = 5, we have: . b \:=\:\tfrac{3}{4}(5) \:=\:\tfrac{15}{4}


    The equation of the entire hyperbola is: . \frac{x^2}{5^2} - \frac{y^2}{(\frac{15}{4})^2} \;=\;1


    We want only the right branch: . \frac{x^2}{25} - \frac{16y^2}{225} \;=\;1\;\;\text{ for }x \ge 5

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. An Exercise
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 15th 2011, 09:47 AM
  2. Set exercise
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: June 19th 2010, 09:37 AM
  3. Exercise
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 25th 2009, 03:59 AM
  4. Help with an exercise
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 10th 2009, 11:35 PM
  5. can you help me with this exercise?
    Posted in the Business Math Forum
    Replies: 0
    Last Post: November 8th 2008, 03:18 AM

Search Tags


/mathhelpforum @mathhelpforum