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Chapter 11: Q. 114 (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 isx216+y236=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 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 equation of the ellipse

From the given graph center at the origin.

The major axis is on y-axis with endpoints0,-6,(0,6).So,b=6鈬�b2=36.

The minor axis is on x-axis with endpoints

-4,0,(4,0).So,role="math" localid="1645530673898" a=4鈬�a2=16.

Hence, the equation of the ellipse is

x216+y236=1.

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