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Q 13.

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Precalculus Enhanced with Graphing Utilities

Found in: Page 677

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problem, identify the graph of each equation without completing the squares.
$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$

The equation represents graph of an ellipse.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

An equation is $6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$ .

Step 2. Identify the graph.

The equation $A x^{2} + C y^{2} + D x + E y + F = 0$ where $A$ and $C$ both cannot be zero,

(a) Defines a parabola if $A C = 0$ .

(b) Defines an ellipse (or a circle) if $A C > 0$ .

(c) Defines a hyperbola if $A C < 0$

Comparing the given equation with the equation $A x^{2} + C y^{2} + D x + E y + F = 0$ we can see that $A = 6$ and $C = 3$ So, we get $A C = 18$ .

Since $A C > 0$ , the given equation is the equation of an ellipse.

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