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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

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.

9 x 2 + 4 y 2 = 1

To determine

(a)

To find:

The vertices, foci and eccentricity of an ellipse

Explanation

Given:

The equation of an ellipse is

9x2+4y2=1

Approach:

For an ellipse with foci on y axis

x2b2+y2a2=1,a>0,b>0

The vertices are (0,±a).

The foci are (0,±c),c2=a2b2

The eccentricity is

e=ca

Calculation:

The standard form of given ellipse is

x2(13)2+y2(12)2=1

This gives a=12,b=13.

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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