Gilbert_Hmwk11sol

Gilbert_Hmwk11sol - moseley(cmm3869 HW11 Gilbert(56380 This...

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moseley (cmm3869) – HW11 – Gilbert – (56380) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – fnd 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. y 2 2 y + x 1 = 0 2. y 2 + 2 y + x 1 = 0 3. x 2 + 2 x y 1 = 0 4. y 2 + 2 y x 1 = 0 5. x 2 + 2 x + y 1 = 0 6. x 2 2 x y 1 = 0 7. x 2 2 x + y 1 = 0 correct 8. y 2 2 y x 1 = 0 Explanation: The graph is that oF a parabola opening downwards 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 simplifcation 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 3 4 1 2 1 2 1 2 3 4 1. 9 x 2 + 18 x + 4 y 2 + 8 y = 23 2. 9 x 2 18 x + 4 y 2 8 y = 23 3. 4 x 2 8 x 9 y 2 18 y = 31 4. 9 x 2 18 x + 4 y 2 + 8 y = 23 correct 5. 4 x 2 8 x 9 y 2 + 18 y = 31 6. 4 x 2 + 8 x 9 y 2 18 y = 31 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 4 + ( y + 1) 2 9 = 1 ,
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moseley (cmm3869) – HW11 – Gilbert – (56380) 2 which after expansion and simpliFcation can be rewritten as 9 x 2 18 x + 4 y 2 + 8 y = 23 . keywords: graph, conic section, ellipse, shifted ellipse 003 10.0 points Which one of the following conic sections has graph 2 4 2 4 6 2 4 2 4 6 1. 4 x 2 8 x y 2 + 2 y = 1 2. y 2 + 2 y 4 x 2 8 x = 7 3. 4 x 2 8 x + y 2 2 y + 1 = 0 4. 4 x 2 + 8 x y 2 2 y = 1 correct 5. 4 x 2 + 8 x + y 2 + 2 y + 1 = 0 6. 4 x 2 + 8 x y 2 + 2 y = 1 7. y 2 + 2 x 4 x 2 8 y = 7 8. y 2 2 x 4 x 2 8 x = 7 Explanation: The graph is a shifted hyperbola having asymptotes which intersect at ( 1 , 1) as well as vertices at (0 , 1) and ( 2 , 1). Thus one equation for this hyperbola is ( x + 1) 2 1 ( y + 1) 2 4 = 1 , which after expansion and simpliFcation can be rewritten as 4 x 2 + 8 x y 2 2 y = 1 . keywords:
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This note was uploaded on 04/12/2011 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.

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Gilbert_Hmwk11sol - moseley(cmm3869 HW11 Gilbert(56380 This...

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