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Q 8.

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Precalculus Enhanced with Graphing Utilities

Found in: Page 676

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

True or False
The equation $a x^{2} + 6 y^{2} - 12 y = 0$ defines an ellipse if width="36" style="max-width: none; vertical-align: -5px;" $a > 0$

The statement is true.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

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

Step 2. State whether the statement is true or false.

The ellipse is given by the equation given below.

$a x^{2} + 6 y^{2} - 12 y = 0$

The ellipse is characterized by negative value of $B^{2} - 4 A C$ .

$\begin{array}{rcl} B^{2} - 4 A C & = & {(0)}^{2} - 4 (a) (6) \\ = & - 24 a \end{array}$

The range of $a$ can be determined for which the given equation is an ellipse.

$\begin{array}{rcl} B^{2} - 4 A C & < & 0 \\ - 24 a & < & 0 \\ a & > & 0 \end{array}$

The given equation is an ellipse if for $a > 0$ , therefore the statement is True.

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