HW4S - Gauthier Joseph – Homework 4 – Due 3:00 am –...

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Unformatted text preview: Gauthier, Joseph – Homework 4 – Due: Sep 20 2007, 3:00 am – Inst: JEGilbert 1 This print-out should have 15 questions. Multiple-choice 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 = 31 2. 4 x 2- 8 x- 9 y 2 + 18 y = 31 3. 9 x 2 + 18 x + 4 y 2- 8 y = 23 4. 9 x 2- 18 x + 4 y 2 + 8 y = 23 5. 4 x 2 + 8 x- 9 y 2 + 18 y = 31 6. 9 x 2- 18 x + 4 y 2- 8 y = 23 correct 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 4 + ( y- 1) 2 9 = 1 , which after expansion and simplification can be rewritten as 9 x 2- 18 x + 4 y 2- 8 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- 2- 4- 6 1. x 2 + 2 x- 4 y 2- 8 y = 7 correct 2. x 2- 2 x + 4 y 2- 8 y + 1 = 0 3. 4 y 2 + 8 y- x 2- 2 x = 1 4. x 2- 2 x- 4 y 2 + 8 y = 7 5. 4 y 2- 8 x- x 2- 2 x = 1 6. x 2 + 2 x + 4 y 2 + 8 y + 1 = 0 7. 4 y 2 + 8 x- x 2- 2 y = 1 8. x 2 + 2 x- 4 y 2 + 8 y = 7 Explanation: The graph is a shifted hyperbola having asymptotes which intersect at (- 1 ,- 1) as well as vertices at (1 ,- 1) and (- 3 ,- 1). Thus one equation for this hyperbola is ( x + 1) 2 4- ( y + 1) 2 1 = 1 , Gauthier, Joseph – Homework 4 – Due: Sep 20 2007, 3:00 am – Inst: JEGilbert 2 which after expansion and simplification can be rewritten as x 2 + 2 x- 4 y 2- 8 y = 7 . 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 ,- 3). 1. x 2 = 3 y 2. x 2 + 12 y = 0 correct 3. x 2 = 12 y 4. x 2 + 3 y = 0 5. x 2 = 8 y 6. x 2 + 8 y = 0 Explanation: keywords: 004 (part 1 of 1) 10 points Suppose you start at the origin in 3-space, move along the x-axis a distance of 6 units in the positive direction, and then move down- ward a distance of 2 units. What are the coordinates of your position? 1. (6 , ,- 2) correct 2. (6 , , 2) 3. (0 ,- 2 , 6) 4. (0 , 6 ,- 2) 5. (6 ,- 2 , 0) Explanation: We start at the origin, which has coordi- nates (0 , , 0). First we move 6 units along the positive x-axis, affecting only the x- coordinate, bringing us to the point (6 , , 0)....
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HW4S - Gauthier Joseph – Homework 4 – Due 3:00 am –...

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