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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q50. (page 677)

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.
$4 x^{2} + 12 x y + 9 y^{2} - x - y = 0$

Short Answer

Expert verified

The equation defines parabola.

Step by step solution

01

Step 1. Given Information

The given equation is $4 x^{2} + 12 x y + 9 y^{2} - x - y = 0$

Here $A = 4, B = 12, C = 9$

02

Step 2. Identifying Conic

$B^{2} - 4 A C = 12^{2} - 4 (4) (9) B^{2} - 4 A C = 144 - 144 = 0$

The equation defines parabola.

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Most popular questions from this chapter

To complete the square of $x^{2} - 3 x$ , add $______$ .

The point that is symmetric with respect to the y-axis to the point $(- 2, 5)$ is $_____$ .

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3 x^{2} + 2 x y + y^{2} + 4 x - 2 y + 10 = 0

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40. $11 x^{2} + 10 \sqrt{3} x y + y^{2} - 4 = 0$

In Problem, identify the graph of each equation without completing the squares.

$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$

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