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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

SKILLS

Graphing Ellipse 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 grapg of the ellipse.

4 x 2 + 25 y 2 = 100

To determine

a)

To find:

The vertices, foci and eccentricity of the given equation of ellipse.

Explanation

Given:

The given equation of an ellipse is,

4x2+25y2=100

Approach:

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

x2a2+y2b2=1

Here, a and b are constant values.

Expression to find vertices is,

V=(±a,0)

Expression to find Foci is,

F=(±c,0),

Here, c2=a2b2

Expression to find Eccentricity (e),

e=ca

Calculation:

Consider the given equation of the ellipse,

4x2+25y2=100

To express the above equation as the basic equation of ellipse, divide by 100 on both side,

4x2100+25y2100=100100x225+y24=1 ……(1)

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

a2=25a=±5

And,

b2=4b=±2

Find the vertices,

To determine

b)

The lengths of the major and minor axes.

To determine

c)

To sketch:

A graph of the given equation of the ellipse.

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