course MTH 272 05/09, 1830 assignment #024024.
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16:42:47 Query problem 7.2.52 (was 7.2.48) identify quadric surface z^2 = x^2 + y^2/2.
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RESPONSE --> z^2 = x^2 + y^2/2 x^2 + y^2/2 -z^2=0 Elliptic cone confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:43:38 What is the name of this quadric surface, and why?
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RESPONSE --> Elliptic Cone Equation matches form for elliptic cone with all variables squared, one being subtracted, and equaling zero. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:46:34 Give the equation of the xz trace of this surface and describe its shape, including a justification for your answer.
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RESPONSE --> xz-trace (y=0): x^2 + (0^2)/2 - z^2=0 x^2 - z^2=0 For this equation to work, z and x must be equal. I think that this trace may only be a single point instead of a shape, particularly since the equation is set equal to zero. confidence rating #$&* 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:48:15 Describe in detail the z = 2 trace of this surface.
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RESPONSE --> x^2 + y^2/2 - z^2 =0 x^2 +y^2/2 =z^2 x^2 + y^2/2 = 4 x^2/4 + y^2/8=1 Ellipse confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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