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Chapter 11: Q. 106 (page 1118)

In the following exercises, graph each ellipse.

x29+y2=1

Short Answer

Expert verified

The Graph of the given ellipse is given by

Step by step solution

01

Step 1.Given information

The equation of the ellipse is

x29+y2=1

02

Step 2.  Concept used

The standard form of the ellipse

with Center at the origin is

x2a2+y2b2=1a>b鈬�majoraxisisx-axiswithendpoints-a,0,(a,0)b>a鈬�majoraxisisy-axis.withendpoints(0,-b,(0,b)

03

Step 3.Find the center and major axis

x29+y2=1Givenx29+y21=1Rewritetheequation

Compare the given equation with the standard form of the ellipse

Center:(0,0),9>1anda2=9鈬�a=卤3b2=1鈬�b=卤1

Major axis:

Onx- axis with endpoints(-3,0),(3,0).

Minor axis

On y-axis with endpoints(0,-1),(0,1).

04

Step 4. Sketch the graph

The graph of the ellipse is

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