Please use justification for each step. (b) Using one of your parameterizations from part (a), compute the area of the region boundedby C, x = 0 and y = %.(c) Starting with the standard equation for this ellipse in rectangular coordinates, convert topolar coordinates. If possible, find r(0).(d) Rotate C about the x-axis to generate a solid. Set up, but do not evaluate, an integral tocompute the surface area of this solid usingi. one of the parameterizations in part (a)ii. polar coordinatesiii. rectangular coordinates(e) Which description of C is easiest to use to compute the surface area of the solid in part(d)? Explain. If possible, compute the surface area using one or more of the integrals setup in (d). Let C be an ellipse centered at the origin with horizontal axis of length 2a and vertical axis oflength 2b, where a, b > 0.(a) Find two distinct unit-speed parameterizations of C.

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Answered: (b) Using one of your parameterizations…

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(b) Using one of your parameterizations from part (a), compute the area of the region bounded by C, x = 0 and y = %.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter7: Conic Sections

Section7.2: Ellipses

Problem 1E: An ellipse is the set of all points in the plane for which the ____ of the distances from two fixed...

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Question

Please use justification for each step.

(b) Using one of your parameterizations from part (a), compute the area of the region bounded
by C, x = 0 and y = %.
(c) Starting with the standard equation for this ellipse in rectangular coordinates, convert to
polar coordinates. If possible, find r(0).
(d) Rotate C about the x-axis to generate a solid. Set up, but do not evaluate, an integral to
compute the surface area of this solid using
i. one of the parameterizations in part (a)
ii. polar coordinates
iii. rectangular coordinates
(e) Which description of C is easiest to use to compute the surface area of the solid in part
(d)? Explain. If possible, compute the surface area using one or more of the integrals set
up in (d).

Let C be an ellipse centered at the origin with horizontal axis of length 2a and vertical axis of
length 2b, where a, b > 0.
(a) Find two distinct unit-speed parameterizations of C.

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