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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

35-38 Graphing Ellipses Use a graphing device to graph the ellipse.

x 2 + 2 y 2 = 8 .

To determine

To sketch:

A graph of the given equation of the ellipse.

Explanation

Approach:

The basic equation for an ellipse with a horizontal major axis which is used is as follows,

x2a2+y2b2=1

Where a and b are constant values.

Expression to find Foci is,

F=(±c,0),

Where, c2=a2b2

Formula to find major axis,

MajorAxis=2a

Formula to find minor axis,

MinorAxis=2b

Calculation:

Consider the given equation of the ellipse,

x2+2y2=8

Further simplify the above equation.

x28+2y28=1x28+y24=1

Compare the above equation with the basic equation for an ellipse and find the vertices as follows,

a2=8a=±8

And

b2=4b=±2

Calculate the value of c as follows,

c2=a2b2c2=84c2=4c=±2

Find the foci,

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Chapter 12 Solutions

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