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Q46.

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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 Problems 43–52, identify the graph of each equation without applying a rotation of axes.
$2 x^{2} - 3 x y + 2 y^{2} - 4 x - 2 = 0$

The equation defines ellipse.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given equation is $2 x^{2} - 3 x y + 2 y^{2} - 4 x - 2 = 0$

Here $A = 2, B = - 3, C = 2$

Step 2. Identifying Conic

$B^{2} - 4 A C = {(- 3)}^{2} - 4 (2) (2) B^{2} - 4 A C = 9 - 16 = - 7 < 0$

The equation defines ellipse.

Most popular questions for Math Textbooks

In Problems 15–18, the graph of a hyperbola is given. Match each graph to its equation.

Equations: $(A) \frac{x^{2}}{4} - y^{2} = 1 (B) x^{2} - \frac{y^{2}}{4} = 1 (C) \frac{y^{2}}{4} - x^{2} = 1 (D) y^{2} - \frac{x^{2}}{4} = 1$

Graph:

True or False

The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .

In Problems 67–74, analyze each conic

$\frac{{(x - 3)}^{2}}{4} - \frac{y^{2}}{25} = 1$

Semi elliptical Arch Bridge The arch of a bridge is a semi ellipse with a horizontal major axis. The span is $30$ feet, and the top of the arch is $10$ feet above the major axis. The roadway is horizontal and is $2$ feet above the top of the arch. Find the vertical distance from the roadway to the arch at $5$ -foot intervals along the roadway.

In Problems 31– 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40. $4 x^{2} - 4 x y + y^{2} - 8 \sqrt{5} x - 16 \sqrt{5} y = 0$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
$2 x^{2} - 3 x y + 2 y^{2} - 4 x - 2 = 0$

Step by Step Solution

Step 1. Given Information

Step 2. Identifying Conic

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.2x2-3xy+2y2-4x-2=0

Step by Step Solution

Step 1. Given Information

Step 2. Identifying Conic

Most popular questions for Math Textbooks

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In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
$2 x^{2} - 3 x y + 2 y^{2} - 4 x - 2 = 0$