Explanation Given info: An ellipse in x z plane is ( x 2 ) 2 + ( z 3 ) 2 = 1 is translated to have center ( 3 , 1 , 5 ) . Concept used: Parametric from of ellipse ( x a ) 2 + ( z b ) 2 = 1 is x = a Cos θ and z = b Sin θ where Q ∈ [ 0 , 2 π ] Calculation: First find the parametric form of ellipse when is in x z plane. x = 2 Cos θ y = 0 z = 3 Sin θ ( Parametric form of ( x a ) 2 + ( z b ) 2 = 1 is x = a Cos θ , y = 0 and z = b Sin θ where Q ∈ [ 0 , 2 π ] initial center of ellipe = ( 0 , 0 , 0 ) ) r → ( Q ) = ( 0.2 Cos θ , 3 Sin θ ) When this ellipse translate parallel to self to center ( 3 , 1 , 5 ) .This can be break into three part. (1) First: ( 0 , 0 , 0 ) to ( 3 , 0 , 0 ) parallel to x − axis. In this translation only x − co-ordinate change but y and z co-ordinate remain constant so Previous parametric form ( 2 Cos θ , 0 , 3 Sin θ ) change to ( 3 + 2 Cos θ , 0 , 3 Sin θ ) ...

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Chapter 14.1, Problem 47E

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Find a parameterization of the ellipse

${(\frac{x}{2})}^{2} + {(\frac{z}{3})}^{2} = 1$ In the $x z$ plane translated to have center $(3, 1, 5)$

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Chapter 14.1, Problem 46E

Chapter 14.1, Problem 48E

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Chapter 14 Solutions

EBK CALCULUS

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

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Find a parameterization of the ellipse ( x 2 ) 2 + ( z 3 ) 2 = 1 In the x z plane translated to have center ( 3 , 1 , 5 )

Solution Summary: The author explains the parametric form of the ellipse in x z plane.

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Find a parameterization of the ellipse

${(\frac{x}{2})}^{2} + {(\frac{z}{3})}^{2} = 1$ In the $x z$ plane translated to have center $(3, 1, 5)$

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Chapter 14 Solutions

Find a parameterization of the ellipse ( x 2 ) 2 + ( z 3 ) 2 = 1 In the x z plane translated to have center ( 3 , 1 , 5 )

Solution Summary: The author explains the parametric form of the ellipse in x z plane.

Videos

Find a parameterization of the ellipse (x2)2+(z3)2=1 In the xz plane translated to have center (3,1,5)

Want to see the full answer?

Chapter 14 Solutions

Find a parameterization of the ellipse

${(\frac{x}{2})}^{2} + {(\frac{z}{3})}^{2} = 1$ In the $x z$ plane translated to have center $(3, 1, 5)$