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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

(a)Use the discriminant to determine whether the graph of the following equation is a parabola, an ellipse, or a hyperbola:

5 x 2 + 4 x y + 2 y 2 = 18

(b) Use rotation of axes to eliminate the x y -term in the equation.

(c) Sketch a graph of the equation.

(d) Find the coordinates of the vertices of this conic (in the x y -coordinate system).

To determine

(a).

To find:

Whether the graph of the following equation is a parabola, an ellipse, or a hyperbola:

5x2+4xy+2y2=18

Explanation

Given:

An equation of a conic section as, 5x2+4xy+2y2=18.

Approach:

Compare the given equation of the conic with the general equation of the conic,

Ax2+Bxy+Cy2+Dx+Ey+F=0

The quantity B24AC is known as discriminant of the above equation,

i. If B24AC>0, then the above equation is of hyperbola equation.

ii. If B24AC=0, then the above equation is of parabola equation.

iii. If B24AC<0, then the above equation is of an ellipse equation.

Calculation:

Given equation of conic is 5x2+4xy+2y2=18

To determine

(b).

To find:

The equation of the given conic after removing the xy-term, use the rotation of axes.

To determine

(c).

To Sketch:

A graph of the equation 5x2+4xy+2y2=18.

To determine

(d).

To find:

The coordinates of the vertices of the conic 5x2+4xy+2y2=18.

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Chapter 12 Solutions

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Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.1 P-49ESect-12.1 P-50ESect-12.1 P-51ESect-12.1 P-52ESect-12.1 P-53ESect-12.1 P-54ESect-12.1 P-55ESect-12.1 P-56ESect-12.1 P-57ESect-12.1 P-58ESect-12.1 P-59ESect-12.1 P-60ESect-12.1 P-61ESect-12.1 P-62ESect-12.1 P-63ESect-12.1 P-64ESect-12.1 P-65ESect-12.1 P-66ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 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