SME
Calculus III (Multivariable) · Problem type
Name the quadric surface
Use this for “Name the surface x² + y² − z² = 1.”
Sort
Count the squared terms and their signs; a variable to the first power means a paraboloid.
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Assumptions
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A quadric is a surface whose equation has squares of x, y and z (or a variable to the first power).
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The traces, slices by planes x = k, y = k or z = k, are ellipses, parabolas or hyperbolas, and they name it.
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Unequal coefficients stretch the surface but do not change its name.
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