Explanation Given info. Two given planes are y = 1 2 x 2 + y 2 + z 2 = 1 Concept used: Intersection of a plane and sphere is circle equation of circle can be parameterized easily. Calculation: y = 1 2 → ( 1 ) x 2 + y 2 + z 2 = 1 → ( 2 ) To find the equation of curve formed by intersection of ( 1 ) and (2) . Put the value of y in ( 2 ) . x 2 + z 2 = 1 − y 2 x 2 + x 2 = 1 − ( 1 2 ) 2 = 1 − 1 4 = 3 4 x 2 + z 2 = 3 4 , This is equation of circle lies in a plane parallel to x z and passing through y = 1 2 ...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.1, Problem 45E

To determine

Find a parameterization of the curve, formed by the intersection of the plane $y = \frac{1}{2}$ with the sphere $x^{2} + y^{2} + z^{2} = 1$ .

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Chapter 14.1, Problem 44E

Chapter 14.1, Problem 46E

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Chapter 14 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

Knowledge Booster

Find a parameterization of the curve, formed by the intersection of the plane y = 1 2 with the sphere x 2 + y 2 + z 2 = 1 .

Solution Summary: The author explains the parametric equation of curved formed by intersection of the plane y = 1 2 with the sphere x 2 +

Find a parameterization of the curve, formed by the intersection of the plane $y = \frac{1}{2}$ with the sphere $x^{2} + y^{2} + z^{2} = 1$ .

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Chapter 14 Solutions

Find a parameterization of the curve, formed by the intersection of the plane y = 1 2 with the sphere x 2 + y 2 + z 2 = 1 .

Solution Summary: The author explains the parametric equation of curved formed by intersection of the plane y = 1 2 with the sphere x 2 +

Find a parameterization of the curve, formed by the intersection of the plane y=12 with the sphere x2+y2+z2=1.

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Chapter 14 Solutions

Find a parameterization of the curve, formed by the intersection of the plane $y = \frac{1}{2}$ with the sphere $x^{2} + y^{2} + z^{2} = 1$ .