Ahyperbola has its center at (0,0)a vertex of (0,19) and an asymptote of y=19/16^x find the equation that describes the hyperbola.

Hyperbola centered at the origin, vertex (0,19), asymptote y = (19/16) x

The axis is the y axis so this hyperbola has the form

We have (0,19) on the hyperbola so a=19.  I'm going to take a wild guess that b=16 so our hyperbola has equation:

How do we find the asymptote?  I don't remember, it's going to be approximately the line from the origin to some point with really big x and y.

As x gets big the +1 will matter less and less, so the asymptote is

Our guess was right!

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

hope this !

step-by-step explanation: