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Quadric Surfaces

EudecioGabriel
in Homework Help

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Question: Sectioning a paraboloid for a plane perpendicular to it's axis and the three units of the vertice, we find an ellipsis of axis equal to 6 and 12 units. Write the equation of the paraboloid.

 

I don't even know how to start!

 

 

Thank you!

As far as I can tell they expect you to use the general equation for an elliptic paraboloid

 

[latex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=z[/latex]

 

Where a and b are the length of the elipsis on the x and y axis respectively. So in this case there are 2 possible equations without more info.

 

[latex]\frac{x^{2}}{6^{2}}+\frac{y^{2}}{12^{2}}=z[/latex]

 

[latex]\frac{x^{2}}{12^{2}}+\frac{y^{2}}{6^{2}}=z[/latex]

Edited by fiveworlds

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