   Chapter 12.5, Problem 16E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 15-28 ■Graphing a Rotated Conic (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the xy-term. (c) Sketch the graph. x y + 4 = 0

To determine

a)

Whether the graph of the equation is a parabola, an ellipse, or a hyperbola by the use of discriminant.

Explanation

Given:

The equation is xy+4=0.

Approach:

The graph of the general equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is either a conic or a degenerate conic. In the non degenerate cases, the graph is

1. If B24AC=0, then the graph is a parabola.

2. If B24AC<0, then the graph is an ellipse.

3. If B24AC>0, then the graph is a hyperbola.

Here, the B24AC is the discriminant.

Calculation:

The equation is

xy+4=0

On comparing the general equation,

A=0,B=1,C=

To determine

b)

The equation without xy-term by the use a rotation of axes.

To determine

c)

To sketch:

The graph of the equation xy+4=0.

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