Lecture 10-6

# Lecture 10-6 - Example x 2-y 2 z 2 4 =-1 4 C...

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10.6 Cylinders and Quadric Surfaces Cylinders Any equation that contains only 2 of 3 variables. The 3rd is unrestricted. Example 1 x 2 + z 2 = 4 Example 2 yz = 1 Do. Sketch y = x 2 . 1

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Quadric Surfaces defn. A quadric surface is a 2nd degree equation in 3 variables, x , y , and z . I. All 3 Variables Squared A. Ellipsoid/Sphere Example 9 x 2 + 16 y 2 + 144 z 2 = 144 2
B. Hyperboloids 1. One Sheet - 1 negative coefficient Example 9 x 2 + 36 z 2 - 4 y 2 = 36 3

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2. Two Sheets - 2 negative coefficients

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Unformatted text preview: Example x 2-y 2 + z 2 4 =-1 4 C. Elliptic/Circular Cone Example z 2 9 = x 2 4-y 2 5 II. 2 Variables Squared (Paraboloids) A. Elliptic Paraboloid Example x + y 2 4 =-z 2 9 6 B. Hyperbolic Paraboloid Example z = x 2-y 2 7 Do. 1. x 2 + y 2 + z 2 = 4 2.-x 2 + y 2 + z 2 = 4 3.-x 2-y 2 + z 2 = 4 4. x 2-y 2 + z 2 = 0 5. x 2-y 2 = 4 6. x = y 2 + z 2 8...
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