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Chapter 10: Q. 10 (page 654)

For the ellipse x225+y29=1, the value of a is _____ , the value of b is _____ , and the major axis is the ____ -axis.

Short Answer

Expert verified

For the ellipse x225+y29=1, the value of a is 5, the value of b is 3 , and the major axis is the x-axis.

Step by step solution

01

Step 1. Given Information

We want to fill the gap in the given equation with the missing terms.

02

Step 2. Method to find:

We know that

If an ellipse is given with the following equation.

x2b2+y2a2=1

where a>b, then it is centred at the origin, the major axis is the y-axis and the parameters aandbrepresent its width: 2aand its height: 2b

03

Step 3. Determining the values of a and b:

From the previous step it is given that a>band then a2>b2

Therefore, for x225+y29=1

Since 25>9it follows that

25=52=a2鈬�a=5and

9=32=b2鈬�b=3

04

Step 4. Determine the major axis:

Since the greater value between aandbis under the variable xsquared it follows that the major axis is thex-axis.

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