Results 1 to 2 of 2

Thread: Another ellipse question...

  1. December 19th 2007, 08:29 AM #1
    free_to_fly
    free_to_fly is offline
    Member
    Joined
    Mar 2007
    From
    England
    Posts
    104

    Another ellipse question...

    I'm stuck on yet another problem...

    The point P(acost, bsint) on the ellipse with the equation:
    x^2/(a^2)+y^2/(b^2)=1
    is joined to the point A (a.0) and M is the mid-point of AP. As t varies, find a cartesian equation of the locus of M.

    Can anyone help please?
    Follow Math Help Forum on Facebook and Google+
  2. December 19th 2007, 08:40 AM #2
    JaneBennet
    JaneBennet is offline
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    The midpoint of the straight line joining P(a\cos{t},b\sin{t}) and A(a,0) is

    M\left(\frac{a\cos{t}+a}{2},\frac{b\sin{t}+0}{2}\r ight)

    So, for the locus of M, we have

    x\ =\ \frac{a}{2}\,(\cos{t}+1)

    y\ =\ \frac{b}{2}\,\sin{t}

    Eliminate t and you have the Cartesian equation for the locus of M.
    Follow Math Help Forum on Facebook and Google+
« Triangular pyramids | Arc length and chord length »

Similar Math Help Forum Discussions

  1. Ellipse question
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 20th 2011, 02:09 AM
  2. Ellipse Question
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 19th 2009, 12:24 PM
  3. Another ellipse question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 20th 2007, 12:32 PM
  4. Ellipse question
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 18th 2007, 03:52 PM
  5. One Last question about ellipse
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 8th 2007, 01:22 PM

Search Tags


/mathhelpforum @mathhelpforum