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# hw 11 - rhodes(ajr2283 HW11 Gilbert(56380 This print-out...

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rhodes (ajr2283) – HW11 – Gilbert – (56380) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which one of the following conic sections has graph 1 2 3 1 1 2 1 2 1. x 2 2 x + y 1 = 0 2. x 2 2 x y 1 = 0 correct 3. x 2 + 2 x y 1 = 0 4. x 2 + 2 x + y 1 = 0 5. y 2 + 2 y + x 1 = 0 6. y 2 + 2 y x 1 = 0 7. y 2 2 y + x 1 = 0 8. y 2 2 y x 1 = 0 Explanation: The graph is that of a parabola opening upwards and having vertex at (1 , 2). Thus it is the graph of y + 2 = A ( x 1) 2 , for some A > 0. But the graph intersects the y -axis at y = 1 so A = 1. Consequently, the graph is that of the conic section ( x 1) 2 y + 2 = 0 , which after expansion and simplification can be rewritten as x 2 2 x y 1 = 0 . keywords: graph, conic section, parabola, shifted parabola, 002 10.0 points Which one of the following conic sections has graph 1 2 1 2 3 4 1 2 3 4 1 2 1. 4 x 2 + 8 x + 9 y 2 + 18 y = 23 2. 9 x 2 18 x 4 y 2 + 8 y = 41 3. 9 x 2 + 18 x 4 y 2 + 8 y = 41 4. 4 x 2 8 x + 9 y 2 18 y = 23 5. 9 x 2 + 18 x 4 y 2 8 y = 41 6. 4 x 2 + 8 x + 9 y 2 18 y = 23 correct Explanation: The graph is a shifted ellipse centered at ( 1 , 1) whose major axis has length 6 and minor axis has length 4. Thus one equation for this ellipse is ( x + 1) 2 9 + ( y 1) 2 4 = 1 ,

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rhodes (ajr2283) – HW11 – Gilbert – (56380) 2 which after expansion and simplification can be rewritten as 4 x 2 + 8 x + 9 y 2 18 y = 23 . keywords: graph, conic section, ellipse, shifted ellipse 003 10.0 points Which one of the following conic sections has graph 2 4 6 2 4 2 4 6 2 4 1. y 2 2 x 4 x 2 + 8 y = 7 2. 4 x 2 + 8 x + y 2 + 2 y + 1 = 0 3. 4 x 2 8 x y 2 2 y = 1 4. 4 x 2 8 x y 2 + 2 y = 1 5. y 2 + 2 x 4 x 2 + 8 x = 7 6. 4 x 2 + 8 x y 2 2 y = 1 7. 4 x 2 8 x + y 2 2 y + 1 = 0 8. y 2 2 y 4 x 2 + 8 x = 7 correct Explanation: The graph is a shifted hyperbola having asymptotes which intersect at (1 , 1) as well as vertices at (1 , 3) and (1 , 1). Thus one equation for this hyperbola is ( y 1) 2 4 ( x 1) 2 1 = 1 , which after expansion and simplification can be rewritten as y 2 2 y 4 x 2 + 8 x = 7 . keywords: graph, conic section, ellipse, shifted ellipse 004 10.0 points Classify the quadric surface x z y 1. hyperbolic paraboloid 2. elliptic paraboloid 3. two-sheeted hyperboloid correct 4. ellipsoid 5. elliptic cone 6. one-sheeted hyperboloid Explanation:
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hw 11 - rhodes(ajr2283 HW11 Gilbert(56380 This print-out...

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