Find parameterizations for the following paths from the point (1, 0, 0) to the point (−1, 0, 0).(a) A straight line segment.(b) A semicircle of radius 1 in the plane y = 0. There are two options; pick the one for which z is always negative.(c) A quarter-circle of radius √2 with center at (0, −1, −1).(d) Any curve of your choice that also passes through the point (0, 1, 2). Find parameterizations for the following paths from the point (1,0,0) to the point (-1, 0, 0).(a) A straight line segment.(b) A semicircle of radius 1 in the plane y = 0. There are two options; pick the one forwhich z is always negative.(c) A quarter-circle of radius √2 with center at (0, -1, −1).(d) Any curve of your choice that also passes through the point (0, 1, 2).

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Answered: Find parameterizations for the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CT: Chapter Test

Problem 8CT

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Question

Find parameterizations for the following paths from the point (1, 0, 0) to the point (−1, 0, 0).
(a) A straight line segment.
(b) A semicircle of radius 1 in the plane y = 0. There are two options; pick the one for which z is always negative.
(c) A quarter-circle of radius √2 with center at (0, −1, −1).
(d) Any curve of your choice that also passes through the point (0, 1, 2).