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Math Help - Calc help asap

  1. #1
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    Calc help asap

    The graph of an ellipse is x^2-xy+y^2 = 3 is shown. What are the dimensions and the location of the box containing the ellipse.

    note: the sides of the box are vertical and horizontal and also are tangent to the ellipse.

    I NEED HELP. I went about to find the derivative first but I honestly have no idea on where to go from here on.. please help
    Last edited by mr fantastic; October 20th 2009 at 06:52 PM. Reason: Included important missing information
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  2. #2
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    Quote Originally Posted by savni98 View Post
    The graph of an ellipse is x^2-xy+y^2 is shown. What are the dimensions and the location of the box containing the ellipse.

    note: the sides of the box are vertical and horizontal and also are tangent to the ellipse.

    I NEED HELP. I went about to find the derivative first but I honestly have no idea on where to go from here on.. please help
    you have to find the equations of the two vertical tangents and the two horizontal tangents

    for the horizontal tangents, y' = 0

    for the vertical tangents, y' is undefined.
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  3. #3
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    hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2
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  4. #4
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    Quote Originally Posted by savni98 View Post
    hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2
    sub those back into the original curve equation and solve
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  5. #5
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    yeah, i did that too and im getting weird values like x^2=3 so x=+-sqrt3 and y^2=1 so y=+-1 for the y'=0. and i get x^2=3/5 so x=+-sqrt3/5 and y^2=3/10 so y=+-sqrt3/10 for the y'=undefined. do those seem reasonable?
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  6. #6
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    Quote Originally Posted by savni98 View Post
    hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2
    this is incorrect
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  7. #7
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    nvm i corrected myself and for the first part y'=0 i got x=+-1 and y=+-2. but for the y'=undefined, im kinda confused, don't you just set the bottom of the derivative to 0?
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    heyy sorry now i got all 4 points, but from there how do i find the actual location of the box and the dimensions??
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  9. #9
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    Quote Originally Posted by savni98 View Post
    heyy sorry now i got all 4 points, but from there how do i find the actual location of the box and the dimensions??
    Draw a box around the ellipse and label the points you have found. Now use simple geometry to get the dimensions of the box.
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    well since the ellipse is tilted and therefore not symetrically to the x and y axis, the points i found are not the vertices of the box and i think when i drew it out, the points i got were actually tangent to the box. how do i go about finding the actual vertices.
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  11. #11
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    Quote Originally Posted by savni98 View Post
    well since the ellipse is tilted and therefore not symetrically to the x and y axis, the points i found are not the vertices of the box and i think when i drew it out, the points i got were actually tangent to the box. how do i go about finding the actual vertices.
    Quote Originally Posted by skeeter View Post
    you have to find the equations of the two vertical tangents and the two horizontal tangents
    [snip]
    The box is bounded by these four lines! Draw the ellipse, draw the lines, get the box.
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