Problem 58 Describe one similarity and one ... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

3 Edition

Chapter 7: Problem 58

Describe one similarity and one difference between the graphs of $\frac{x^{2}}{9}-\frac{y^{2}}{1}=1$ and $\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$

Short Answer

Expert verified

The similarity between the graphs of these two equations is that they both have the same semi-axes lengths, which are 1 and 3. The difference is that the hyperbola defined by $\frac{x^{2}}{9}-\frac{y^{2}}{1}=1$ opens horizontally, while that defined by $\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$ opens vertically.

Step by step solution

Identify the orientation of the first equation

For the equation $\frac{x^{2}}{9}-\frac{y^{2}}{1}=1$, the 'x' term comes first and is positive, meaning the hyperbola opens along the x-axis (horizontally). The difference in the denominators of the x and y terms signifies the length of the semi-axes a and b, being 鈭�9 = 3 and 鈭�1=1, respectively.

Identify the orientation of the second equation

In the equation $\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$, however, the 'y' term comes first and is positive. This means that the hyperbola created from this equation will open along the y-axis (vertically). The lengths of the semi-axes would still be 鈭�1 = 1 and 鈭�9 =3, respectively.

Formulate the Similarity and Difference

The similarity between these two hyperbolas is that they both have the same length for their semi-axes, which are 1 and 3. The difference, however, is their orientation. The first hyperbola is oriented horizontally while the second one is oriented vertically.

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91影视

Describe one similarity and one difference between the graphs of \(\frac{x^{2}}{9}-\frac{y^{2}}{1}=1\) and \(\frac{y^{2}}{9}-\frac{x^{2}}{1}=1\)

Short Answer

Step by step solution

Identify the orientation of the first equation

Identify the orientation of the second equation

Formulate the Similarity and Difference

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