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Chapter 11: Q 11.46. (page 1111)

Short Answer

Expert verified

The graph of an ellipse is shown below:

Step by step solution

01

Step 1. Given information

The given ellipse is (x-1)225+(y+3)216=1.

02

Step 2. Write the equation in standard form.

The standard form of an ellipse with center(h,k) is given by (x-h)2a2+(y-k)2b2=1鈥�(1).

Compare the given equation with standard form and conclude that (x-1)225+(y+3)216=1is in standard form and the center is (1,-3).

03

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

Compare the equation (1)with (x-1)225+(y+3)216=1to find a2and b2.

a2=25b2=16

Since 25>16and 25is in the x2term, the major axis will be horizontal.

04

Step 4. Find the endpoints of the major axis and the minor axis.

The value is a2=25.

This implies that a=卤5.

This follows the distance from the center to the vertices is 5.

The value isb2=16.

This implies that b=4.

This follows that the minor axis is vertical and the distance from the center to the endpoints of the minor axis is 4.

05

Step 5. Draw the ellipse.

The graph of an ellipse is shown below:

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