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Chapter 11: Q. 109 (page 1118)

In the following exercises, graph each ellipse.

16x2+36y2=576

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 16x2+36y2=576

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. Convert into standard form 

16x2+36y2=576Given16x2576+36y2576=576576Dividewith576onbothsidesx236+y216=1Simplify

04

Step 4.Find the center and major axis

x236+y216=1

Compare the given equation with the standard form of the ellipse

Center:(0,0),36>16anda2=36鈬�a=卤6b2=16鈬�b=卤4

Major axis:

Onx-axis with endpoints(-6,0),(6,0).

Minor axis

On y-axis with endpoints(0,-4),(0,4).

05

Step 5. Sketch the ellipse

The graph of the ellipse is shown below

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