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M408m-Luecke_HW3 - romasko(qrr58 Assignment 3 luecke(55035...

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romasko (qrr58) – Assignment 3 – luecke – (55035) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Classify the quadric surface x z y 1. elliptic paraboloid 2. hyperbolic paraboloid 3. two-sheeted hyperboloid correct 4. elliptic cone 5. one-sheeted hyperboloid 6. ellipsoid Explanation: The trace on any horizontal plane, i.e., any plane parallel to the coordinate plane z = c , is always a circle for all | c | ≤ c 0 for some choice of c 0 , while the trace on any plane parallel to the coordinate planes x = 0 and y = 0 is alway a hyperbolas. Consequently the quadric surface is a two-sheeted hyperboloid . keywords: quadric surface, ellipsoid, ellip- tic paraboloid, hyperbolic paraboloid, one- sheeted hyperboloid, two-sheeted hyper- boloid, 002 10.0 points Which one of the following equations has graph when the circular cylinder has radius 2. 1. y 2 + z 2 - 4 y = 0 correct 2. x 2 + y 2 - 2 x = 0 3. x 2 + y 2 + 4 y = 0 4. y 2 + z 2 - 2 y = 0 5. x 2 + y 2 + 2 y = 0 6. x 2 + y 2 - 4 x = 0 Explanation: The graph is a circular cylinder whose axis of symmetry is parallel to the x -axis, so it will be the graph of an equation containing no x -term. This already eliminates the equations x 2 + y 2 + 2 y = 0 , x 2 + y 2 + 4 y = 0 , x 2 + y 2 - 2 x = 0 , x 2 + y 2 - 4 x = 0 .
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