Results 1 to 3 of 3

Math Help - Ellipse help

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Ellipse help

    The arch of an underpass is a semi - ellipse 60ft wide and 20 ft high. find the clearance at the edge of a lane if the edge is 20ft from the middle.

    Backofbook: \frac{20}{3} \sqrt{5} ft
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The arch of an underpass is a semi - ellipse 60ft wide and 20 ft high. find the clearance at the edge of a lane if the edge is 20ft from the middle.

    Backofbook: \frac{20}{3} \sqrt{5} ft
    Don't I love ellipses.

    So the ellipse is horizontal. Its major axis, 2a, is 60 ft. Its minor axis, 2b, is 2*20 ft.
    If the center of the ellipse is the center of the lane, then the ellipse is
    (x^2)/(a^2) +(y^2)/(b^2) = 1
    (x^2)/(30^2) +(y^2)/(20^2) = 1 -----(i)

    At the edge of the lane, or at x = 20 ft, what is the y there?
    (20^2)/(30^2) +(y^2)/(20^2) = 1
    Clear the fractions, multiply both sides by (30^2)(20^2),
    (20^2)(20^2) +(y^2)(30^2) = (30^2)(20^2)
    (30^2)(y^2) = (30^2)(20^2) -(20^2)(20^2)
    (30^2)(y^2) = (20^2)(30^2 -20^2)
    (30^2)(y^2) = (20^2)[(30+20)(30-20)]
    (30^2)(y^2) = (20^2)(50*10)
    (30^2)(y^2) = (20^2)(500)
    (30^2)(y^2) = (20^2)(10^2)(5)
    y^2 = [(20^2)(10^2)(5)] / (30^2)
    Take the square roots of both sides,
    y = [(20)(10)sqrt(5)] / 30
    y = 200sqrt(5) / 30
    y = (20/3)sqrt(5) ft. ---------------answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, ^_^Engineer_Adam^_^!

    ticbol provided an excellent solution . . . as usual.
    . . I simplified the arithmetic/algebra.


    The arch of an underpass is a semi-ellipse, 60ft wide and 20 ft high.
    Find the clearance at the edge of a lane if the edge is 20ft from the middle.

    Back of book: \frac{20}{3} \sqrt{5} ft
    This ellipse has: a = 30, b = 20

    The equation is: .x/30 + y/20 .= .1

    . . . . . . . . . . . . . . . . . . . _______
    And we have: . y .= .(2/3)√900 - x

    . . . . . . . . . . . . . . . . . . . ___ . . . . . . . . ._ . . . . . . . . ._
    When x = 20: .y .= .(2/3)√500 .= .(2/3)10√5 .= . (20/3)√5



    I'm still waiting for LaTeX to return . . .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ellipse
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 17th 2010, 06:48 AM
  2. ellipse
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 16th 2010, 11:29 AM
  3. ellipse 2
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 15th 2010, 11:41 AM
  4. ellipse
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 7th 2010, 04:08 PM
  5. Ellipse
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 17th 2008, 05:54 AM

Search Tags


/mathhelpforum @mathhelpforum