(a) Explanation : Consider the given equation, 4 x 2 − y 2 − 8 x − 2 y − 13 = 0 Now compare the above equation with general equation of conic section , A x 2 + C y 2 + D x + E y + F = 0 , A = 4 , C = − 1 , D = − 8 , E = − 2 , F = − 13 The following table represent the classification of Conic Section from its general equation, A x 2 + C y 2 + D x + E y + F = 0 . Classification of Conic Section Condition Circle A = C , A ≠ 0 (b) To determine Whether the graph of the equation x 2 + y 2 − 2 x − 8 = 0 is a circle, a parabola, an ellipse or a hyperbola: (c) To determine Whether the graph of the equation 2 x 2 − 4 x − 3 y − 3 = 0 is a circle, a parabola, an ellipse or a hyperbola: (d) To determine Whether the graph of the equation x 2 + 6 y 2 − 2 x − 5 = 0 is a circle, a parabola, an ellipse or a hyperbola:

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.4, Problem 72E

(a)

To determine

Whether the graph of the equation 4x2−y2−8x−2y−13=0 is a circle, a parabola, an ellipse or a hyperbola,

(b)

To determine

Whether the graph of the equation x2+y2−2x−8=0 is a circle, a parabola, an ellipse or a hyperbola:

(c)

To determine

Whether the graph of the equation 2x2−4x−3y−3=0 is a circle, a parabola, an ellipse or a hyperbola:

(d)

To determine

Whether the graph of the equation x2+6y2−2x−5=0 is a circle, a parabola, an ellipse or a hyperbola:

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Chapter 6.4, Problem 71E

Chapter 6.4, Problem 73E

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Match the equation with its graph.

Chapter 6 Solutions

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Whether the graph of the equation 4 x 2 − y 2 − 8 x − 2 y − 13 = 0 is a circle , a parabola, an ellipse or a hyperbola,

Solution Summary: The author explains that the graph of the equation 4x2-y 2-8x-2y-13=0 is a hyperbola, thus (iv) is correct option.

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Whether the graph of the equation 4x2−y2−8x−2y−13=0 is a circle, a parabola, an ellipse or a hyperbola,

Whether the graph of the equation x2+y2−2x−8=0 is a circle, a parabola, an ellipse or a hyperbola:

Whether the graph of the equation 2x2−4x−3y−3=0 is a circle, a parabola, an ellipse or a hyperbola:

Whether the graph of the equation x2+6y2−2x−5=0 is a circle, a parabola, an ellipse or a hyperbola:

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Chapter 6 Solutions