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Chapter 11: Q 11.43. (page 1110)

Find the equation of the ellipse shown.

Short Answer

Expert verified

The equation of an ellipse is x24+y225=1.

Step by step solution

01

Step 1. Given information

The graph of an ellipse is shown below:

02

Step 2. Determine whether the major axis is horizontal or vertical.

From the given figure, observe that the figure is an ellipse centered at the origin.

So, the equation of an ellipse is x2a2+y2b2=1鈥�(1).

From the figure, observe that the major axis of an ellipse is vertical.

03

Step 3. Find the value of a2 and b2.

The distance from the center to the ellipse is 5.

So, b=5which implies b2=25.

The minor axis is horizontal and the distance from the center to the vertex is 2.

So, a=2which implies a2=4.

04

Step 4. Find the equation of an ellipse.

Substitute the values of a2and b2into the equation (1).

Thus, the equation of an ellipse is as follows:

x24+y225=1

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