Results 1 to 2 of 2

Math Help - This Alg 2 problem is hard

  1. #1
    Junior Member mattballer082's Avatar
    Joined
    Mar 2005
    From
    Los angeles
    Posts
    27

    This Alg 2 problem is hard

    Find the equation of the ellipse specified:

    (a) foci (-2,1) (4,1) and minor axis 8

    (b) vertices (+-4,0) (0,+-5)

    can you explain how to do it?

    Also this extra credit problem is getting me frustrated.

    sketch the graph of the equation and indicate the center, the foci, and the length of axes.

    2x squared + 3y squared + 12x -24y + 60= 0

    do i need to group it and then factor? what would my next steps be?? thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by mattballer082 View Post
    Find the equation of the ellipse specified:

    (a) foci (-2,1) (4,1) and minor axis 8
    Hello,

    the center of the ellipse is the midpoint between the foci: C(1, 1)
    I assume that the axes of the ellipse are parallel to the coordinate axes, otherwise your problem can't be done:
    Let a be the major axis and let be b the minor axis.
    You know that the distance between center and the focus on the major axis is called excentricity e and that it is calculated by:
    e = a - b . Thus e = 4 - 1 = 3

    e + b = a. With your problem:
    9 + 64 = 73 = a. a = √(73)

    Therefore the equation of your ellipse becomes:
    x/73 + y/64 = 1

    Quote Originally Posted by mattballer082 View Post
    (b) vertices (+-4,0) (0,+-5)

    can you explain how to do it?
    The midpoint of all vertices is the center of the ellips: C(0, 0)
    The length of the axes is the distance between center and vertices. Therefore
    a = 4, b = 5

    The equation of the ellipse becomes:

    x/16 + y/25 = 1

    Quote Originally Posted by mattballer082 View Post
    Also this extra credit problem is getting me frustrated.

    sketch the graph of the equation and indicate the center, the foci, and the length of axes.

    2x squared + 3y squared + 12x -24y + 60= 0
    ...
    Firts: Complete the squares:

    2x + 3y + 12x - 24y + 60 = 0
    2(x + 6x + 9 - 9) +3(y - 8y + 16 - 16) = -60
    2(x+3) - 18 + 3(y-4) - 48 = -60
    2(x+3) + 3(y-4) = 6
    (x+3)/3 + (y-4)/2 = 1

    The center of the ellipse is C(-3, 4)

    The major axis is a = √3; the minor axis is b = √2

    e = a - b ==> e = 3 - 2 = 1

    Therefore F1(3+1, 4) and F2(3-1, 4)
    Attached Thumbnails Attached Thumbnails This Alg 2 problem is hard-ellip_mathballer.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Really need help on this hard problem IMO
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 20th 2010, 03:45 AM
  2. A really hard problem!
    Posted in the Math Puzzles Forum
    Replies: 3
    Last Post: September 8th 2009, 12:51 PM
  3. hard problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 19th 2009, 02:40 AM
  4. Help Now Please hard problem!!!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 11th 2007, 07:28 AM
  5. Very hard age problem...
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 1st 2006, 08:18 AM

Search Tags


/mathhelpforum @mathhelpforum