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Please Help Easy conic section question!

  • Thread starter zaboda42
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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

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Re: Please Help!!! Easy conic section question!

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

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Re: Please Help!!! Easy conic section question!

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


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

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Re: Please Help!!! Easy conic section question!

You shouldn't have needed your calculator. [itex]x^2- y^2= 9[/itex] or [itex]x^2/9- y^2/9= 1[/itex] 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.
 

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