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Chapter 11: Q 11.40. (page 1108)

Graph: x29+y216=1.

Short Answer

Expert verified

The graph of an ellipse is shown below:

Step by step solution

01

Given Information

The given ellipse is x29+y216=1.

02

Step 2. Write the equation in standard form.

The standard form of an ellipse isx2a2+y2b2=1鈥�(1).

Compare the given equation with standard form and conclude that x29+y216=1is in standard form.

03

Step 3. Find whether the major axis is horizontal or vertical.

Compare the equation (1)with x29+y216=1to find a2and b2.

a2=9b2=16

Since localid="1645598655011" 16>9and localid="1645598713177" 16is in the y2term, the major axis will be vertical.

04

Step 4. Find the endpoints of the major axis.

The endpoints will be the y-intercepts.

Since b2=16, b=卤4.

Thus, the coordinates of the endpoints of the major axis are (0,4)and (0,-4).

05

Step 5. Find the endpoints of the minor axis.

The endpoints will be the x-intercepts.

Since a2=9, a=卤3.

Thus, the coordinates of the endpoints of the minor axis are (3,0)and (-3,0).

06

Step 6. Draw the ellipse.

The graph of an ellipse is shown below:

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