   Chapter 12.2, Problem 20E ### 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

# SKILLS9-28 ■ Graphing Ellipses An equation of an ellipse is given. (a) Find the vertices, foci, and eccentricity of the ellipse. (b) Determine the lengths of the major and minor axes. (c) Sketch a graph of the ellipse. 2 x 2 + 49 y 2 = 98

To determine

(a)

To find:

The vertices, foci and eccentricity of the ellipse.

Explanation

Given:

The equation of ellipse is,

2x2+49y2=98

Approach:

The following equation is the basic equation for an ellipse that is not centered at the origin.

(xh)2a2+(yk)2b2=1

With the following properties,

Vertices V=(±ah,0k) ……(1)

Foci F=(±ch,0k) ……(2)

Eccentricity e=ca ……(3)

Where

c2=a2b2 ……(4)

Calculation:

Consider the equation,

2x2+49y2=98

Convert the equation of the ellipse to the standard equation.

2(x0)298+49(y0)298=1(x0)249+(y0)22=1(x0)272+(y0)2(2)2=1

Compare the equation of the ellipse with the standard equation.

a=7b=2h=0k=0

Calculate the vertices of the ellipse.

Substitute 7 for a, 0 for h and 0 for k in equation (1).

V1=(70,00)=(7,0)

Substitute 7 for a, 0 for h and 0 for k in equation (1).

V2=(70,00)=(7,0)

Calculate the value of c

To determine

(b)

The length of the major and minor axes.

To determine

(c)

To sketch:

The graph of the ellipse.

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