Easy conic section question

[zaboda42]

Please Help! Easy conic section question!

1. Graph each equation. Identify the conic section and its lines of symmetry. Then find the domain and range.



2. x^2 - y^2 - 9 = 0



3. I have no idea how to do this. I know it's a hyperbola because i solved for "y" and graphed it in my calculator, but i have no idea how to find the domain/range and values. Help!

 

[symbolipoint]

That is a hyperbola centered at the origin. Add +9 to both sides of the equation and then divide both sides by +9. I do not remember how to handle the rest of the graphing but the methods and characteristics should be well discussed and exemplefied in your book.

 

[Mentallic]

There are two ways I can think of to answer this problem. The first is much easier, but only useful if you can visualize the hyperbola's rough shape.

1) Convert it into: $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$
With this hyperbola, if you understand its shape, you can find its domain such that $$x\leq a$$ and $$x\geq a$$ since the intersections are at $$x=\pm a$$


2) Solve for y and find (if any) undefined regions, such as divisions by 0 or negatives in the square roots. This will give you the domain. (no undefined regions means that the domain is all x)
For the range, solve for x and do the same procedure.

 

[HallsofIvy]

You shouldn't have needed your calculator. $x^2- y^2= 9$ or $x^2/9- y^2/9= 1$ is the standard form for a hyperbola with center at (0,0) and vertices at (3,0) and (-3,0). Knowing those vertices should give you the domain immediately.