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Homework Help: Multivariable calculus question

  1. Oct 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Sketch the following curves on separate number planes.

    y= 2x^2

    x^2 + 2y^2= 4

    2. Relevant equations



    3. The attempt at a solution

    For the first one, would the intersection of the curve with the y axis be at y=2 ( I have attached a diagram of my solution). The minimum point would be at (0,2)???

    For the second one, what do we do with the 2 which is the coefficient of y^2. Would the 4 be the radius of the circle.

    Thanks in advance.
     

    Attached Files:

  2. jcsd
  3. Oct 20, 2007 #2
    In the first one. If the curve was intersecting the y-axis, then x = 0 at the point of intersection, and so y = 0 aswell, so it intersects are (0,0). Also, the minimum point of the function is at (0,0).

    For the second one, are you sure that the equation you have describes a circle? I would call it an ellipse myself.
     
  4. Oct 20, 2007 #3
    oh alrite, but then what happens with the 2 in x^2 for the first equation. Yea, the second one is an ellipse so would 4 be the radius?? Cheers
     
  5. Oct 20, 2007 #4
    [tex] y = 2x^2 [/tex]
    if x = 0; [tex] y = 2*(0^2) = 0 [/tex]

    As for the ellipse. have you tried working out the values for x and y when the other one is set to 0? That will tell u where it crosses each axis.

    edit: This might help - http://en.wikipedia.org/wiki/Ellipse
     
    Last edited: Oct 20, 2007
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