Explanation Given information : The equation of quadratic surface, x 2 = y 2 + 3 z 2 . Graph : The graph of the quadratic surface x 2 = y 2 + 3 z 2 can be sketched using the traces, For the plane x = 0 , the trace of the surfaces is, x 2 = y 2 + 3 z 2 0 = y 2 + z 2 ( 1 3 ) 2 whichis a pointyz plane. For the plane x = k , the trace of the surfaces is, x 2 = y 2 + 3 z 2 k 2 = y 2 + z 2 ( 1 3 ) 2 which is an ellipse in the plane parallel to yz plane and k is a constant. For the plane y = k , the trace of the surfaces is, x 2 = y 2 + 3 z 2 x 2 = k 2 + z 2 ( 1 3 ) 2 x 2 − z 2 ( 1 3 ) 2 = k 2 which is a hyperbola in plane parallel to xz plane and k is a constant. For the plane z = k , the trace of the surfaces is, x 2 = y 2 + 3 z 2 x 2 = y 2 + 3 k 2 x 2 − y 2 = 3 k 2 which is a hyperbola in plane parallel to xy plane and k is a constant. Since, traces are point in yz plane,an ellipse in plane parallel to yz plane and hyperbolas in planes parallel to xz and xypalnes , the graph of quadratic surface is provided below, Interpretation : 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

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 9.7, Problem 43PS

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To graph: The quadratic surface x2=y2+3z2 and identify the surface

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Chapter 9.7, Problem 42PS

Chapter 9.7, Problem 44PS

Chapter 9 Solutions

Calculus

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To graph : The quadratic surface x 2 = y 2 + 3 z 2 and identify the surface

Solution Summary: The author illustrates the graph of the quadratic surface x2=y 2+3z2.

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To graph: The quadratic surface x2=y2+3z2 and identify the surface

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Chapter 9 Solutions