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Unformatted text preview: miller (zdm77) assignment 3 luecke (58600) 1 This printout should have 15 questions. Multiplechoice 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 1 2 1 2 3 1 1. y 2 + 2 y + x 1 = 0 2. x 2 + 2 x + y 1 = 0 3. x 2 2 x + y 1 = 0 4. y 2 + 2 y x 1 = 0 5. y 2 2 y + x 1 = 0 correct 6. x 2 2 x y 1 = 0 7. y 2 2 y x 1 = 0 8. x 2 + 2 x y 1 = 0 Explanation: The graph is that of a parabola opening to the left and having vertex at (2 , 1). Thus it is the graph of ( y 1) 2 = A ( x 2) , for some A > 0. But the graph also passes through (1 , 2), so A = 1. Consequently, the graph is that of the conic section ( y 1) 2 + x 2 = 0 , which after expansion and simplification can be rewritten as y 2 2 y + x 1 = 0 . keywords: graph, conic section, parabola, shifted parabola, 002 10.0 points Find an equation for the parabola having vertex (0 , 0) and focus (0 , 2). 1. x 2 = 3 y 2. x 2 + 8 y = 0 correct 3. x 2 = 8 y 4. x 2 + 2 y = 0 5. x 2 = 2 y 6. x 2 + 3 y = 0 Explanation: The parabola with equation x 2 = 4 ay has focus (0 , a ) and vertex (0 , 0). Conse quently, when a = 2, the parabola has equa tion x 2 + 8 y = 0 . 003 10.0 points Find an equation of the ellipse. Then find its foci. 4 8 4 8 4 8 4 8 x y miller (zdm77) assignment 3 luecke (58600) 2 1. x 2 64 + y 2 49 = 1, foci: parenleftBig 15 , parenrightBig 2. x 2 49 + y 2 64 = 1, foci: parenleftBig , 15 parenrightBig correct 3. x 2 49 + y 2 64 = 113, foci: parenleftBig , 15 parenrightBig 4. x 2 8 + y 2 7 = 1, foci: parenleftBig 15 , parenrightBig 5. x 2 7 + y 2 8 = 1, foci: parenleftBig , 15 parenrightBig Explanation: keywords: 004 10.0 points Find the vertices, foci and asymptotes of the hyperbola 2 x 2 3 y 2 + 24 x 30 y = 9 . 1. vertices: parenleftBig 6 3 , 5 parenrightBig , foci: parenleftBig 6 5 , 5 parenrightBig , asymptotes: y + 5 = radicalbigg 2 3 ( x + 6) correct 2. vertices: parenleftBig 6 3 , 5 parenrightBig...
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 Fall '07
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