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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 an ellipse is given. (a) Find the axis, vertices and eccentricity of an ellipse. (b)Find the length of the major and minor axis of an ellipse. (c) Sketch a graph of the ellipse.

y 2 = 1 2 x 2

To determine

(a)

To find:

The vertices, foci and eccentricity of an ellipse whose equation is y2=12x2.

Explanation

Approach:

For an ellipse with foci on the 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 the given ellipse is

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

This gives a=1,b=12

To determine

(b)

To find:

The length of the major and the minor axis of the ellipse y2=12x2.

To determine

(c)

To find:

The sketch of an ellipse y2=12x2.

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