# Quiz 6 - Or if ”'3’ 4&6 Version 002/AAAAC w DGQOGC...

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Unformatted text preview: Or.) if ”'3’ 4&6 Version 002 /AAAAC w DGQOGC —- Gilbert - (78759) - 1 This printout should have 3 questions. Multiplechoice questions may continue on the next column or page W find all choices before answering. 001 10.0 points Determine which one of the following equa— tions has graph 1 y2 =zw~1 2 m~y2m1 3 10—22 =1 4 22 zyml 5. 2:2-1—2 m1 6. (9—532 2 lcorrect Explanation: The graph is a cylinder with axis parallel to the z»axis. In addition its trace on the my—plane is a parabola opening in the positive y—direction and having positive y—intercept. Consequently, the graph is that of the equa— tion keywords: quadric surface, graph of equation, cylinder, 3D graph, paraboiic cylinder, 002 10.0 points Find a parameterization of the horizontal circie of radius 4 having center (2, 5, m1). 1. r(t) = (2m4sint)i~(5+4cost)j—k 2. r(t) 2 (2+4sint)i+(5m4cost)j+k 3. r(t) m (2— 4sint)i+ (5+4cost)j w k correct 4. r(t) w (2+4cost)i~i~5j+(l~4sént)k 5. r(t) = ((2w4cost)i~5j+(l+4sint)k 6. r(t) = (2+4cost)i+5jw(lm4sint)k Explanation: if the vector function r(t) m 33(t) i ~+~ y(t)j + z(t) k traces out a horizontal circle having center (2, 5, —1), then z(t) 2 —1 for all t because the circle must lie in the horizontal plane z(t) : m1. On the other hand, the projection red) = \$(t)i+y(t)j of this circle on the mywplane is a circie of radius 4 having center at (2, 5, 0). Thus, as as circle in the my—plane it has the equation (m——2)2+(y—5)2 m is. Consequentiy, (2305) W 2)2 + (W) - 5V = 16, andso r(z';) = (2m4sint)i+(5+4cost)j—— k is one parametrization of the horizontal circle of radius 4 and center (2, 5, , ~1). keywords: vector function, space curve, circle, plane, radius, center circle, 003 10.0 points Version 002/AAAAC ~— DGQOGC — Gilbert W (78759) ' Find an equation for the plane passing through the point P(5, 3, 6) and perpendicu— lar to the z—axis. 1. y :2 ~3 2. a: = m5 3. z 7—— ﬁcorrect 4. y = 3. 5. :1: = 5 6. z x —6 Explanation: If the plane is perpendicular to the z—axis, then it is of the form 2: 2 d. But if this plane also passes through P(5, 3, 6), then it has equation ...
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