Explanation Approach: The graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is 1. a parabola if B 2 − 4 A C = 0 , 2. an ellipse if B 2 − 4 A C < 0 , 3. a hyperbola if B 2 − 4 A C > 0 . Here, the quantity B 2 − 4 A C is called the discriminant of the equation To determine (b) To find: The equation of the conic after eliminating the x y − term using the rotation of axis. To determine (c) To sketch: The graph of the conic.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 12.CR, Problem 69E

To determine

(a)

To find:

Whether the graph of the equation x2+4xy+y2 =1 is a parabola, an ellipse, or a hyperbola using the discriminant.

To determine

(b)

To find:

The equation of the conic after eliminating the xy− term using the rotation of axis.

To determine

(c)

To sketch:

The graph of the conic.

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Chapter 12.CR, Problem 68E

Chapter 12.CR, Problem 70E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

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) To find: Whether the graph of the equation x 2 + 4 x y + y 2 = 1 is a parabola, an ellipse, or a hyperbola using the discriminant.

Solution Summary: The author explains that the graph of the equation x2+4xy+y=1 is a hyperbola.

Videos

(a)

To find:

Whether the graph of the equation x2+4xy+y2 =1 is a parabola, an ellipse, or a hyperbola using the discriminant.

(b)

To find:

The equation of the conic after eliminating the xy− term using the rotation of axis.

(c)

To sketch:

The graph of the conic.

Want to see the full answer?

Chapter 12 Solutions

(a) To find: Whether the graph of the equation x 2 + 4 x y + y 2 = 1 is a parabola, an ellipse, or a hyperbola using the discriminant.

Solution Summary: The author explains that the graph of the equation x2+4xy+y=1 is a hyperbola.

Videos

(a) To find: Whether the graph of the equation x2+4xy+y2 =1 is a parabola, an ellipse, or a hyperbola using the discriminant.

(b) To find: The equation of the conic after eliminating the xy− term using the rotation of axis.

(c) To sketch: The graph of the conic.

Want to see the full answer?

Chapter 12 Solutions

(a)

To find:

Whether the graph of the equation x2+4xy+y2 =1 is a parabola, an ellipse, or a hyperbola using the discriminant.

(b)

To find:

The equation of the conic after eliminating the xy− term using the rotation of axis.

(c)

To sketch:

The graph of the conic.