Explanation Given information : The quadric surface, z 2 = 1 + x 2 9 + y 4 2 . Calculation : Consider, the equation of quadric surface, z 2 = 1 + x 2 9 + y 4 2 . This equation can be written in standard form as, z 2 = 1 + x 2 9 + y 4 2 x 2 9 + y 4 2 − z 2 = − 1 x 2 3 2 + y 2 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. Hyperbola shaped traces are found in x z and y z coordinate planes. No trace of the surface in x y coordinate plane

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 9.7, Problem 40PS

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The type, traces of quadric surface given by the equation z2=1+x29+y42 and also graph the equation.

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Chapter 9.7, Problem 39PS

Chapter 9.7, Problem 41PS

Chapter 9 Solutions

Calculus

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

Solution Summary: The author analyzes the quadric surface's traces and graphs. The standard equation of the sphere is cz2.

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The type, traces of quadric surface given by the equation z2=1+x29+y42 and also graph the equation.

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Chapter 9 Solutions