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Chapter 11: Q. 99 (page 1118)

In the following exercises, graph each ellipse.

x24+y225=1.

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

x24+y225=1.

02

Step 2. Concept used

The standard form of the ellipse with

center (0,0)is

localid="1645422226494" x2a2+y2b2=1

  • a>b鈬�major axis onx-axis with x-intercepts-a,0,(a,0).
  • b>a鈬�major axis on y-axis with y-intercepts0,-b,(0,b).
03

Step 3. Find the center and major axis

x24+y225=1

Compare with the standard form of the ellipse

Center0,0.

Here,9>4

a2=4鈬�a=卤2b2=9鈬�b=卤3

So,

y-axis is the major axis with endpoints localid="1645424530502" 0,-3,(0,3).

and

x-axis is the minor axis with endpoints-2,0,(2,0).

04

Step 4. Graph the ellipse

The graph of the ellipse is shown below.

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