Assignment 6 - patino (mp25752) – Assignment6 – luecke...

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Unformatted text preview: patino (mp25752) – Assignment6 – luecke – (57510) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points This question is from section 13.6. Find an equation for the surface obtained by rotating the parabola x = y 2 about the x-axis. 1. z 2 − y 2 = x 2. y 2 + z 2 = x correct 3. y 2 − z 2 = x 4. x 2 − z 2 = y 5. x 2 + y 2 = z Explanation: The surface of paraboloid of revolution (cir- cular paraboloid) with vertex at the origin, axis the x-axis and opens to the right. Thus the trace in the xz plane is also a parabola: x = z 2 , and equation for surface is y 2 + z 2 = x . 002 10.0 points Hint: This is from Chapter 13. Use the distance formula to write down the conditions described on a point (x,y,z). This will give you the equation for such points. Find an equation for the surface consisting of all points P ( x, y, z ) equidistant from the point P ( − 3 , , 0) and the plane x = 3. 1. 12 z 2 + x 2 = 12 y 2. y 2 − z 2 + 12 x = 0 3. y 2 − x 2 = 6 z 4. y 2 + z 2 + 12 x = 0 correct 5. y 2 + 12 x 2 = 1 Explanation: The distance from P ( x, y, z ) to the point P ( − 3 , , 0) is radicalBig ( x − − 3) 2 + ( y − (0)) 2 + ( z − 0) 2 , while the distance from P ( x, y, z, ) to the plane x = 3 is | x − 3 | . When these distances are equal, therefore, | x − 3 | = radicalBig ( x − − 3) 2 + ( y − (0)) 2 + ( z − 0) 2 . Consequently, after squaring both sides and simplifying we see that the set of all equi- distant points P ( x, y, z ) is the surface y 2 + z 2 + 12 x = 0 . keywords: plane, locus, equidistant from point and plane 003 10.0 points Find a vector function whose graph is the curve of intersection of the sphere x 2 + y 2 + z 2 = 8 and the plane y = 2 ....
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This note was uploaded on 10/21/2009 for the course M 53215 taught by Professor Lueke during the Spring '09 term at University of Texas at Austin.

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Assignment 6 - patino (mp25752) – Assignment6 – luecke...

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