HW3 - Valencia (drv252) – assignment 3 – luecke –...

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Unformatted text preview: Valencia (drv252) – assignment 3 – luecke – (58600) 1 This print-out should have 15 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 − 1 − 2 1 2 3 − 1 1. x 2 − 2 x + y − 1 = 0 2. y 2 + 2 y − x − 1 = 0 3. y 2 − 2 y + x − 1 = 0 correct 4. x 2 + 2 x + y − 1 = 0 5. y 2 − 2 y − x − 1 = 0 6. x 2 + 2 x − y − 1 = 0 7. x 2 − 2 x − y − 1 = 0 8. y 2 + 2 y + x − 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 , − 4). 1. x 2 + 16 y = 0 correct 2. x 2 = 15 y 3. x 2 + 4 y = 0 4. x 2 + 15 y = 0 5. x 2 = 4 y 6. x 2 = 16 y Explanation: The parabola with equation x 2 = 4 ay has focus (0 , a ) and vertex (0 , 0). Conse- quently, when a = − 4, the parabola has equa- tion x 2 + 16 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 Valencia (drv252) – assignment 3 – luecke – (58600) 2 1. x 2 4 + y 2 25 = 29, foci: parenleftBig , ± √ 21 parenrightBig 2. x 2 2 + y 2 5 = 1, foci: parenleftBig , ± √ 21 parenrightBig 3. x 2 5 + y 2 2 = 1, foci: parenleftBig ± √ 21 , parenrightBig 4. x 2 25 + y 2 4 = 1, foci: parenleftBig ± √ 21 , parenrightBig 5. x 2 4 + y 2 25 = 1, foci: parenleftBig , ± √ 21 parenrightBig correct 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 ± √ 5 , − 5 parenrightBig , foci: parenleftBig − 6 ± √ 3 , − 5 parenrightBig , asymptotes: y + 5 = ± radicalbigg 3 2 ( x + 6) 2. vertices: parenleftBig − 6 ± √ 3 , − 5 parenrightBig , foci: parenleftBig...
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This note was uploaded on 03/26/2009 for the course CH 302 taught by Professor Holcombe during the Spring '07 term at University of Texas at Austin.

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HW3 - Valencia (drv252) – assignment 3 – luecke –...

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