Results 1 to 5 of 5

Math Help - Questions on conic sections

  1. #1
    Rae
    Rae is offline
    Newbie
    Joined
    Nov 2010
    Posts
    12

    Questions on conic sections

    1) Describe the curve traced out by a point 2 feet from the top of an 8-foot ladder as the bottom of the ladder moves away from a vertical wall.

    Thank you
    Last edited by Rae; November 28th 2010 at 01:39 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Rae View Post
    1) Describe the curve traced out by a point 2 feet from the top of an 8-foot ladder as the bottom of the ladder moves away from a vertical wall.
    Take the origin to be at the base of the wall. When the ladder makes an angle \theta with the wall, the coordinates (x,y) of the point 2 feet from the top of the ladder are (x,y) = (2\sin\theta, 6\cos\theta). (Draw a diagram to make sure that you understand why that is.) Thus \sin\theta = \frac12x and \cos\theta = \frac16y. Now use the fact that \sin^2\theta + \cos^2\theta = 1 to get an equation connecting x and y.
    Last edited by Opalg; November 27th 2010 at 04:57 AM. Reason: Corrected serious mistake
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Rae
    Rae is offline
    Newbie
    Joined
    Nov 2010
    Posts
    12
    Could you explain how you get (x,y) = (2sin theta, 6cos theta) ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Rae View Post
    Could you explain how you get (x,y) = (2sin theta, 6cos theta) ?
    Did you draw a diagram, as I suggested???

    \setlength{\unitlength}{2mm}<br />
\begin{picture}(40,40)<br />
\put(5.5,23.5){$\bullet$}<br />
\put(0.5,28){$ \theta$}<br />
\put(4.5,26.5){$2$}<br />
\put(15,13){$ 6$}<br />
\put(7,24){$(x,y)$}<br />
\put(6,0){\line(0,1){24}}<br />
\put(0,24){\line(1,0){6}}<br />
\thicklines<br />
\put(0,0){\line(0,1){40}}<br />
\put(0,0){\line(1,0){40}}<br />
\put(24,0){\line(-3,4){24}}<br />
\end{picture}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Rae
    Rae is offline
    Newbie
    Joined
    Nov 2010
    Posts
    12
    I did draw a diagram, but I guess I was thinking about the problem wrong because I didn't see it that way. Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conic Sections
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 14th 2010, 10:07 PM
  2. Conic Sections
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 7th 2009, 05:22 AM
  3. Conic sections
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 3rd 2009, 09:58 AM
  4. conic sections
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 23rd 2008, 05:22 AM
  5. Conic sections
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: January 31st 2008, 05:09 AM

Search Tags


/mathhelpforum @mathhelpforum