   Chapter 12.5, Problem 30E ### 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

# 29-32 Identifying a Conic from Its Discriminate (a) Use the discriminate to identify the conic. (b) Confirm your answer by graphing the conic using a graphic device. x 2 − 2 x y + 3 y 2 = 8

To determine

(a)

The conic x22xy+3y2=8 by using its discriminant.

Explanation

Given:

The equation is,

x22xy+3y2=8(1)

Approach:

The graph of equation Ax2+Bxy+Cy2+Dx+Ey+F=0 represents

1) a parabola if B24AC=0.

2) an ellipse if B24AC<0.

3) a hyperbola if B24AC>0.

Roots of a quadratic equation ax2+bx+c=0 are given by x=b±b24ac2a.

Calculation:

Compare Equation (1) with Ax2+Bxy+Cy2+Dx+Ey+F=0

To determine

(b)

To sketch:

The graph of the conic using a graphing device.

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