Explanation Given information : The quadric surface, 9 x 2 + 4 y 2 + z 2 = 1 . Calculation : Consider, the equation of quadric surface, 9 x 2 + 4 y 2 + z 2 = 1 . This equation can be written in standard form as, 9 x 2 + 4 y 2 + z 2 = 1 x 2 1 9 + y 2 1 4 + z 2 1 = 1 x 2 ( 1 3 ) 2 + y 2 ( 1 2 ) 2 + z 2 1 2 = 1 Since we know the standard equation of the sphere is x 2 + y 2 + z 2 = r 2 , where r is the radius of the sphere. The standard equation of ellipsoid is x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 , where a , b and c are constants. Ellipse shaped traces are found in coordinate planes. The standard equation of elliptic paraboloidis z = x 2 a 2 + y 2 b 2 , where a and b are constants. Parabola shaped traces are found in x z and y z coordinate planes. Trace is just a point in x y coordinate plane. z -axis is the axis for the elliptic paraboloid with the equation provided above. The standard equation of hyperbolic paraboloidis z = y 2 b 2 − x 2 a 2 , where a and b are constants. Parabola shaped traces are found in x z and y z coordinate planes. Trace are intersecting lines in x y coordinate plane. The standard equation of hyperboloid of one sheet is x 2 a 2 + y 2 b 2 − z 2 c 2 = 1 , where a , b and c are constants. Hyperbola shaped traces are found in planes parallel to x z and y z coordinate planes. Trace is an ellipse lines in x y coordinate plane. z -axis is the axis for hyperboloid of one sheet with the equation provided above. The standard equation of hyperboloid of two sheets is x 2 a 2 + y 2 b 2 − z 2 c 2 = − 1 , where a , b and c are constants

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 9.7, Problem 31PS

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The type, traces of quadric surface given by the equation 9x2+4y2+z2=1 and also graph the equation.

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Chapter 9.7, Problem 30PS

Chapter 9.7, Problem 32PS

Chapter 9 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 9.1 - Prob. 1PS Ch. 9.1 - Prob. 2PS Ch. 9.1 - Prob. 3PS Ch. 9.1 - Prob. 4PS Ch. 9.1 - Prob. 5PS Ch. 9.1 - Prob. 6PS Ch. 9.1 - Prob. 7PS Ch. 9.1 - Prob. 8PS Ch. 9.1 - Prob. 9PS Ch. 9.1 - Prob. 10PS

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08 - Conic Sections - Hyperbolas, Part 1 (Graphing, Asymptotes, Hyperbola Equation, Focus); Author: Math and Science;https://www.youtube.com/watch?v=Ryj0DcdGPXo;License: Standard YouTube License, CC-BY

The type, traces of quadric surface given by the equation 9 x 2 + 4 y 2 + z 2 = 1 and also graph the equation.

Solution Summary: The author analyzes the traces of quadric surface given by the equation 9x2+4y2, +z2. The standard equation of ellipsoid is

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The type, traces of quadric surface given by the equation 9x2+4y2+z2=1 and also graph the equation.

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Chapter 9 Solutions