Explanation Given: The equation is 13 x 2 + 6 3 x y + 7 y 2 = 16 . Approach: The graph of the general equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is either a conic or a degenerate conic. In the non degenerate cases, the graph is 1. If B 2 − 4 A C = 0 , then the graph is a parabola. 2. If B 2 − 4 A C < 0 , then the graph is an ellipse. 3. If B 2 − 4 A C > 0 , then the graph is a hyperbola. Here, the B 2 − 4 A C is the discriminant. Calculation: The equation is 13 x 2 + 6 3 x y + 7 y 2 = 16 13 x 2 + 6 3 x y + 7 y 2 − 16 = 0 On comparing the general equation, A = 13 , B = 6 3 , C To determine b) The equation without x y -term by the use a rotation of axes. To determine c) To sketch: The graph of the equation 13 x 2 + 6 3 x y + 7 y 2 = 16 .

4th Edition

ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

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Chapter 12.5, Problem 18E

To determine

a)

Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.

To determine

b)

The equation without xy-term by the use a rotation of axes.

To determine

c)

To sketch:

The graph of the equation 13x2+63xy+7y2=16.

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Chapter 12.5, Problem 17E

Chapter 12.5, Problem 19E

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Chapter 12 Solutions

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Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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a) Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.

Solution Summary: The author explains how to determine whether the graph of the equation is a parabola, an ellipse, or by using the discriminant.

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a) Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.

b) The equation without xy-term by the use a rotation of axes.

c) To sketch: The graph of the equation 13x2+63xy+7y2=16.

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Chapter 12 Solutions

a)

Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.

b)

The equation without xy-term by the use a rotation of axes.

c)

To sketch:

The graph of the equation 13x2+63xy+7y2=16.