Chapter 10: Q. 10 (page 654)

For the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , the value of a is ___ , the value of b is _ , and the major axis is the __ -axis.

Short Answer

Expert verified

For the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , the value of a is $5$ , the value of b is $3$ , and the major axis is the $x -$ axis.

Step by step solution

Step 1. Given Information

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

Step 2. Method to find:

We know that

If an ellipse is given with the following equation.

$\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$

where $a > b$ , then it is centred at the origin, the major axis is the y-axis and the parameters $a a n d b$ represent its width: $2 a$ and its height: $2 b$

Step 3. Determining the values of a and b:

From the previous step it is given that $a > b$ and then $a^{2} > b^{2}$

Therefore, for $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$

Since $25 > 9$ it follows that

$25 = 5^{2} = a^{2} \Rightarrow a = 5$ and

$9 = 3^{2} = b^{2} \Rightarrow b = 3$

Step 4. Determine the major axis:

Since the greater value between $a a n d b$ is under the variable $x$ squared it follows that the major axis is the $x - a x i s .$

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For the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , the value of a is ___ , the value of b is _ , and the major axis is the __ -axis.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Method to find:

Step 3. Determining the values of a and b:

Step 4. Determine the major axis:

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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

Step by step solution

Step 1. Given Information

Step 2. Method to find:

Step 3. Determining the values of a and b:

Step 4. Determine the major axis:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

For the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , the value of a is ___ , the value of b is _ , and the major axis is the __ -axis.