Results 1 to 2 of 2

Math Help - How would I do this? I have the answer and most steps but....

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    104

    How would I do this? I have the answer and most steps but....

    Let A be a positive number and define a curve parametrically by
    x(t)=t^3-t and y(t)=A/(1+t^2).
    Note that there is one value of A for which the "self-intersection" of the curve is perpendicular. Please find this A.

    I know the answer is 4, but....I'm having trouble justifying the point of intersection. I know it occurs for t=1 and t=-1, and we get (0, A/2) as the point BUT how do I show this formally? Obviously if t=1 or -1, we get the same point (x,y), but that's just by intuition. How would I do it if it were not so obviously what t values to use? That is, how do I actually find the coordinates of the intersection? I hope this question makes sense?

    I don't need help after that, but here would be the rest:
    I know after that dy/dx=(dy/dt)/(dx/dt). Then we plug in t=1 and t=-1 to get m1 and m2.
    I know I will need m1*m2=-1 since perpendicular.
    So (A/4)(-A/4)=-1, and so, A=4
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    Please try to solve the system

    <br />
x(t_1)=x(t_2)<br />

    and

    <br />
y(t_1)=y(t_2)<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 11th 2011, 04:31 PM
  2. Replies: 2
    Last Post: March 2nd 2010, 08:18 AM
  3. Replies: 3
    Last Post: February 7th 2010, 10:49 AM
  4. Replies: 1
    Last Post: February 4th 2010, 08:09 PM
  5. [SOLVED] Is this answer and steps correct?
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 3rd 2009, 10:34 PM

Search Tags


/mathhelpforum @mathhelpforum