   Chapter 12.2, Problem 25E ### 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

# 9 - 2 8 . Graphing Ellipses An equation of ellipse is given (a) Find the vertices, foci and eccentricity of ellipse. (b) Find the length of major and minor axes. (c) Sketch the graph of an ellipse. x 2 + 4 y 2 = 1

To determine

(a)

To find:

The vertices, foci and eccentricity of an ellipse

Explanation

Given:

The equation of ellipse is

x2+4y2=1

Approach:

For an ellipse with horizontal major axis,

x2a2+y2b2=1,a>0,b>0

The vertices are (±a, 0).

The foci are (±c,0),c2=a2b2

The eccentricity is,

e=ca

Calculation:

The standard form of given ellipse is

x212+y2(12)2=1

This gives, a=1,b=12.

To determine

(b)

To find:

The length of major and minor axis of an ellipse

To determine

(c)

To sketch:

The graph of an ellipse

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