Results 1 to 2 of 2

Math Help - Orthogonal Trajectories

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    4

    Orthogonal Trajectories

    "Find the orthogonal trajectories of the family of curves x^2+y^2=2cx.

    I know the steps: 1) solve for c...okay... c=(x^2+y^2)/2x.
    2)Find y', and plug the c back into it.
    3) set dy/dx equal to the negative reciprocal of y' from pt. 2, and solve for y. This is the family of orth. traj.

    My problem is finding y' for part 2. Well, I can find y', but getting it into a form so that I can solve for y in part 3.

    y=(2cx-x^2)^(1/2)

    y'= 1/(2sqrt((x^2+y^2)/x-x^2)*((x^2+y^2)/x-2x)

    Where should I go from here? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by lakesfan210 View Post
    "Find the orthogonal trajectories of the family of curves x^2+y^2=2cx.

    I know the steps: 1) solve for c...okay... c=(x^2+y^2)/2x.
    2)Find y', and plug the c back into it.
    3) set dy/dx equal to the negative reciprocal of y' from pt. 2, and solve for y. This is the family of orth. traj.

    My problem is finding y' for part 2. Well, I can find y', but getting it into a form so that I can solve for y in part 3.

    y=(2cx-x^2)^(1/2)

    y'= 1/(2sqrt((x^2+y^2)/x-x^2)*((x^2+y^2)/x-2x)

    Where should I go from here? Thanks!
    Have you been taught implicit differentiation:

    2x + 2y \frac{dy}{dx} = 2c \Rightarrow \frac{dy}{dx} = \frac{c - x}{y}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthogonal Trajectories
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: June 26th 2011, 07:15 PM
  2. Orthogonal Trajectories
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 15th 2011, 10:50 PM
  3. Orthogonal Trajectories
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2009, 07:57 AM
  4. Orthogonal Trajectories
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 2nd 2008, 07:18 PM
  5. orthogonal trajectories
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 22nd 2007, 12:29 AM

Search Tags


/mathhelpforum @mathhelpforum