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Chapter 11: Q. 100 (page 1118)

In the following exercises, graph each ellipse.

x29+y225=1.

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

01

Step 1. Given information

The equation of the ellipse isx29+y225=1.

02

Step 2. Conceptused

The standard form of the ellipse with

Center(0,0)is

localid="1645528234928" 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+y225=1

Compare with the standard form of the ellipse

localid="1645434250033" center(0,0)25>9anda2=9鈬�a=卤3b2=25鈬�b=卤5

Major axis:

On y-axis with endpoints(0,-5),(0,5).

Minor axis:

On x-axis with endpoints(-3,0),(3,0).

04

Step 4. Sketch the ellipse

The graph of the ellipse is shown below.

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