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Chapter 11: Q. 102 (page 1118)

In the following exercises, graph each ellipse.
x216+y236=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 isx216+y236=1.

02

Step 2. Concept used

The standard form of the ellipse with

Centre:0,0is

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

x216+y236=1

Compare with the standard form of the ellipse

localid="1645432640134" Center0,0,36>16anda2=16鈬�a=卤4b2=36鈬�b=卤6

Major axis:

Onlocalid="1645425899245" y-axiswith endpoints (0,-6),(0,6).

Minor axis:

Onlocalid="1645426041274" x-axiswithendpoints-4,0),(0,4.

04

Step 4. Graph the ellipse

The graph of the ellipse is

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