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Unformatted text preview: Miller, Kierste – Homework 4 – Due: Sep 20 2007, 3:00 am – Inst: JEGilbert 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Which one of the following conic sections has graph 1 2 3 4 1 2 1 2 3 4 1 2 1. 4 x 2 8 x + 9 y 2 + 18 y = 23 2. 4 x 2 + 8 x + 9 y 2 18 y = 23 3. 9 x 2 + 18 x 4 y 2 + 8 y = 41 4. 9 x 2 18 x 4 y 2 + 8 y = 41 5. 4 x 2 8 x + 9 y 2 18 y = 23 correct 6. 9 x 2 18 x 4 y 2 + 8 y = 41 Explanation: The graph is a shifted ellipse centered at (1 , 1) whose major axis has length 6 and mi nor axis has length 4. Thus one equation for this ellipse is ( x 1) 2 9 + ( y 1) 2 4 = 1 , 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 002 (part 1 of 1) 10 points Which one of the following conic sections has graph 2 4 2 4 6 2 4 6 2 4 1. x 2 2 x 4 y 2 8 y = 7 2. x 2 + 2 x + 4 y 2 8 y + 1 = 0 3. 4 y 2 8 x x 2 + 2 x = 1 4. x 2 + 2 x 4 y 2 + 8 y = 7 5. x 2 + 2 x 4 y 2 8 y = 7 6. x 2 2 x + 4 y 2 + 8 y + 1 = 0 7. 4 y 2 8 y x 2 2 x = 1 correct 8. 4 y 2 + 8 x x 2 + 2 y = 1 Explanation: The graph is a shifted hyperbola having asymptotes which intersect at ( 1 , 1) as well as vertices at ( 1 , 2) and ( 1 , 0). Thus one equation for this hyperbola is ( y 1) 2 1 ( x + 1) 2 4 = 1 , Miller, Kierste – Homework 4 – Due: Sep 20 2007, 3:00 am – Inst: JEGilbert 2 which after expansion and simplification can be rewritten as 4 y 2 8 y x 2 2 x = 1 . keywords: graph, conic section, ellipse, shifted ellipse 003 (part 1 of 1) 10 points Find an equation for the parabola having vertex (0 , 0) and focus (0 , 4). 1. x 2 + 15 y = 0 2. x 2 = 16 y 3. x 2 = 4 y 4. x 2 + 16 y = 0 correct 5. x 2 = 15 y 6. x 2 + 4 y = 0 Explanation: keywords: 004 (part 1 of 1) 10 points Suppose you start at the origin in 3space, move along the xaxis a distance of 4 units in the positive direction, and then move down ward a distance of 8 units. What are the coordinates of your position? 1. (4 , , 8) 2. (4 , , 8) correct 3. (0 , 4 , 8) 4. (4 , 8 , 0) 5. (0 , 8 , 4) Explanation: We start at the origin, which has coordi nates (0 , , 0). First we move 4 units along the positive xaxis, affecting only the x coordinate, bringing us to the point (4 , , 0)....
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 Fall '07
 Gilbert
 Conic section

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