Algebra 2 Help (Hyperbolas and Ellipses)

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Ok for #1: x^2 / 4 - y^2 / 9 = 1

First you want to know what its domain is, or what x-values the function is defined on. That turns out to be (-infinity, -2] and [2, infinity) because any x-value between -2 and 2 would require y^2 / 9 to be less than 0, which is impossible. The hyperbola is of the form (x^2 / a^2) - (y^2 / b^2) so it opens in the x-direction, so it looks something like the solution to #3 but rotated so that it opens up in the x- and negative x-directions

so it looks like this:


#6:

The foci of a hyperbola of form
(x^2 / a^2) - (y^2 / b^2) = 1
are given by (±√(a^2 + b^2), 0)

 

Thanks for the rapid help, but your explanation really confused me . I greatly appreciated the effort put in!

Edit: I understand your explanation now! Thanks Alot!
!