Chapter 4.6, Problem 52E

a.

To determine

To find: The graph of $y^2=121x^2$ is symmetric with respect to the x-axis.

Answer to Problem 52E

The graph is symmetric with respect to x-axis.

Explanation of Solution

Given:

The graph $y^2=121x^2$ .

Calculation:

To show the graph of $y^2=121x^2$ is symmetric with respect to x-axis replace $y$ with $-y$ .

  $\begin{array}{c}{\left(-y\right)}^2=121x^2\\ y^2=121x^2\end{array}$

It can be seen that we get the same equation.

Therefore, the graph is symmetric with respect to x-axis.

b.

To determine

To find : The graph of $y^2=121x^2$ is symmetric with respect to the y-axis.

Answer to Problem 52E

The graph is symmetric with respect to y-axis.

Explanation of Solution

Given:

The graph is,

  $y^2=121x^2$

Calculation:

To show the graph of $y^2=121x^2$ is symmetric with respect to y-axis replace $x$ with $-x$ .

  $\begin{array}{c}{\left(-y\right)}^2=121{\left(-x\right)}^2\\ y^2=121x^2\end{array}$

It can be seen that we get the same equation.

Therefore, the graph is symmetric with respect to y-axis.

c.

To determine

To find: The graph of $y^2=121x^2$ is symmetric with respect to the line $y=x$ .

Answer to Problem 52E

The graph is not symmetric with respect to the line $y=x$ .

Explanation of Solution

Given:

The graph is $y^2=121x^2$ .

Calculation:

To show the graph of $y^2=121x^2$ is symmetric with respect to the line $y=x$ replace the place of $x$ and $y$ .

  $x^2=121y^2$

The above equation is not similar to the given equation.

Therefore, the graph is not symmetric with respect to the line $y=x$ .

d.

To determine

To find: The graph of $y^2=121x^2$ is symmetric with respect to the line $y=-x$ .

Answer to Problem 52E

The graph is not symmetric with respect to the line $y=-x$ .

Explanation of Solution

Given:

The graph is $y^2=121x^2$ .

Calculation:

To show the graph of $y^2=121x^2$ is symmetric with respect to the line $y=-x$ replace $-x$ with $-y$ .

  $\begin{array}{c}{\left(-x\right)}^2=121{\left(-y\right)}^2\\ x^2=121y^2\end{array}$

It can be seen that it is not same as given equation.

Therefore, the graph is not symmetric with respect to the line $y=-x$ .