Alegebraic Testing

[chief94mgmc1518]

Use algebraic tests to determine whether the graph of the equation 4x[sup:1izqwqs1]2[/sup:1izqwqs1]-9y[sup:1izqwqs1]2[/sup:1izqwqs1]= 1 is symmetric with respect to the x axis, y axis, or origin.

 

[mmm4444bot]

Hello Chief:

Are you currently studying Conic Sections?

Please let us know what you're thinking about this exercise, and show any work that you've been able to do, so that we can better know how to help you with these questions.

(There is more than one way to approach this exercise; we would like to guide you using the methods that you're currently studying.)

Cheers,

~ Mark

 

[chief94mgmc1518]

Our class is dealing with Graphing Equations: Point Plotting and symmetry. I really dont know where to start this problem

 

[mmm4444bot]

Our class is dealing with Graphing Equations: Point Plotting and symmetry. I really dont know where to start this problem

Hi Chief:

Thank you for providing this information.

When we are given a relationship between x and y in the form of an equation that does NOT explicitly express y in terms of x, then the first step is to solve the given equation for y.

You will get:

y = [some expression that contains the variable x]

This equation serves as a FORMULA for y.

In other words, to plot a point in this relationship, you pick ANY value for x, and then use the formula to determine the corresponding value of y.

Please show your work on solving the given equation for y.

If you go on to study Conic Sections, then you will recognize that the given equation has a parabola for a graph, AND that this particular parabola has a horizontal axis of symmetry (unlike y = x^2, for example, which has a vertical axis of symmetry).

After you solve the equation for y, then we can explain how you can recognize this symmetry from your result.

Cheers,

~ Mark