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Chapter 11: Q. 113 (page 1118)

In the following exercises, find the equation of the ellipse shown in the graph.

Short Answer

Expert verified

The equation of the ellipse isx29+y216=1.

Step by step solution

01

Step 1.Given information

The graph of the ellipse is

02

Step 2.Concept used

The standard form of the ellipse with a center at the origin isx2a2+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 equation of the ellipse

From the given graph center at the origin.

The major axis is on y-axis with endpoints0,-4,(0,4).So,b=4鈬�b2=16.

The minor axis is on x-axis with endpoints-3,0,(3,0).So,a=3鈬�a2=9.

Hence, the equation of the ellipse is

x29+y216=1.

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