Explanation Given information : The quadratic surface x 2 + y 2 + z 2 = 9 . The general equations of all quadratic surfaces along with the description of their traces is provided below, 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

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 5PS

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Chapter 9.7, Problem 4PS

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Chapter 9 Solutions

Calculus

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To match: The equation of quadratic surface x 2 + y 2 + z 2 = 9 with its graph .

Solution Summary: The author explains the general equations of all quadratic surfaces along with the description of their traces.

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To match: The equation of quadratic surface x2+y2+z2=9 with its graph.

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Chapter 9 Solutions