B 3 points the trace of this surface in the plane z 1

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(b)(3 points)The trace of this surface in the planez= 1is a curve described bythe equationx2+y2=y3. This equation implicitly definesyas a function ofx.Computey0(x)whenx=-2andy= 2.
Math 230 Final Exam SolutionsWinter Quarter 2014Page 12 of 16Question 8(35 points).A surface is defined byx2-y2+z4=-1.(a)(16 points, 4 points each)Sketch its traces in the following planes.Label thepoints of intersection with the coordinate axes.2
Math 230 Final Exam SolutionsWinter Quarter 2014Page 13 of 16(b)(4 points)Set up the coordinate axes correctly and sketch this surface inR3.
(c)(15 points)Find the points on the surfacex2-y2+z4=-1that are closest tothe point(0,0,1).
Math 230 Final Exam SolutionsWinter Quarter 2014Page 14 of 16
Math 230 Final Exam SolutionsWinter Quarter 2014Page 15 of 16

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