Explanation Given information: The equation is A x 2 + B x y + C y 2 + D x + E y + F = 0 . Formula used: If we exclude the degenerate conics, the graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 Where A and C are not both zero, is A parabola if either A = 0 or C = 0 or A C = 0 . An ellipse if A C > 0 . A hyperbola if A C < 0. Proof: By using the rotation axis formulas, the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 can be transformed as A ' x 2 + B ' x y + C ' y 2 + D ' x + E ' y + F ' = 0 And the discriminate B 2 − 4 A To determine (b) To prove: The graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is an ellipse if B 2 − 4 A C < 0 . To determine (c) To prove: The graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is a hyperbola if B 2 − 4 A C > 0 .

Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

2nd Edition

ISBN: 9780321869401

Author: J. S. Ratti

Publisher: PEARSON

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Question

Chapter 8.5, Problem 76E

To determine

(a)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a parabola if B2−4AC=0.

To determine

(b)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is an ellipse if B2−4AC<0.

To determine

(c)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a hyperbola if B2−4AC>0.

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Chapter 8.5, Problem 75E

Chapter 8.5, Problem 77E

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Chapter 8 Solutions

Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

Knowledge Booster

(a) To prove: The graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is a parabola if B 2 − 4 A C = 0 .

Solution Summary: The author explains how the graph of the equation Ax2+Bxy+Cy&Dx+Ey +F=0 is a parabola if B

(a)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a parabola if B2−4AC=0.

(b)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is an ellipse if B2−4AC<0.

(c)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a hyperbola if B2−4AC>0.

Want to see the full answer?

Chapter 8 Solutions

(a) To prove: The graph of the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 is a parabola if B 2 − 4 A C = 0 .

Solution Summary: The author explains how the graph of the equation Ax2+Bxy+Cy&Dx+Ey +F=0 is a parabola if B

(a) To prove: The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a parabola if B2−4AC=0.

(b) To prove: The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is an ellipse if B2−4AC<0.

(c) To prove: The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a hyperbola if B2−4AC>0.

Want to see the full answer?

Chapter 8 Solutions

(a)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a parabola if B2−4AC=0.

(b)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is an ellipse if B2−4AC<0.

(c)

To prove:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is a hyperbola if B2−4AC>0.