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Related Flashcards
Cards In This Set
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Ellipsoid
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X^2/a^2 + y^2/b^2 + z^2/c^2 = 1All Traces are ellipsesIf a=b=c, sphere
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Cone
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Z^2/c^2 = x^2/a^2 + y^2/b^2Horizontal Traces are ellipsesVertical traces in planes x=k and y=k are hyperbolas if k is not 0, a pair of lines if k=0
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Elliptic Paraboloid
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Z/c= x^2/a^2 + y^2/b^2Horizontal Traces are ellipsesvertical traces are parabolasVariable raised to the first power indicates axis of paraboloid
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Hyperboloid of one sheet
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X^2/a^2 + y^2/b^2 - z^2/c^2 = 1Horizontal traces are ellipses vertical traces are hyperbolasaxis of symmetry corresponds with variable whose coefficient is negative
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Hyperbolic Paraboloid
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Z/c= x^2/a^2 - y^2/b^2Horizontal traces are hyperbolasVertical traces are parabolas
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Hyperboloid of two sheets
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-x^2/a^2 - y^2/b^2 + z^2/c^2 = 1Horizontal traces in z=k are ellipses if k>c or k<-cVertical Traces are hyperbolasTwo minus signs indicate two sheets
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