   Chapter 12.2, Problem 2E ### 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

# CONCEPTSAn graph of the equation x 2 a 2 + y 2 b 2 = 1 with a > b > 0 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( ± c , 0 ) , where c = __________. So the graph of x 2 5 2 + y 2 4 2 = 1 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( ____, ____ ) and ( ____, ____ ).

To determine

To fill:

Explanation

Given:

An graph of the equation x2a2+y2b2=1 with a>b>0 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci (±c,0), where c= __________. So the graph of x252+y242=1 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( ____, ____ ) and ( ____, ____ ).

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

Calculation:

Consider the given equation of the ellipse,

x252+y242=1 ……(1)

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

a2=52a=±5

And,

b2=42b=±4

Find the vertices,

V=(±a,0)=(±5,0)=(5,0),(5,0)

Calculate the value of c as follows,

c2=a2b2c2=5242c2=9c=±3

Find the foci,

F=(±c,0)=(±3,0)=(3,0),(3,0)

Therefore, the vertices are (5,0),(5,0) and foci are (3,0),(3,0) and of the given equation of ellipse

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