Multivariable calculus question

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Homework Help Overview

The discussion revolves around sketching curves defined by the equations y = 2x² and x² + 2y² = 4, which fall under the subject area of multivariable calculus. Participants are exploring the characteristics and intersections of these curves on coordinate planes.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to determine the intersection points of the curves with the axes and are questioning the implications of coefficients in the equations. There is discussion about the nature of the second curve, with some suggesting it describes an ellipse rather than a circle.

Discussion Status

The discussion is active, with participants providing insights and questioning each other's interpretations. Some guidance has been offered regarding the intersection points and the nature of the curves, but no consensus has been reached on the specifics of the equations.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the depth of their explorations. There is an ongoing discussion about the definitions and properties of the curves involved.

engineer_dave
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Homework Statement



Sketch the following curves on separate number planes.

y= 2x^2

x^2 + 2y^2= 4

Homework Equations





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.
 

Attachments

  • Curve.JPG
    Curve.JPG
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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.
 
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
 
[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:

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