Question

Which graph represents the hyperbola?

x^2/5^2 - y^2/4^2 = 1

Answer 1

The graph is a horizontal hyperbola with vertices at (-5,0) and (5,0).

Explanation:

The given formula is

`(x^(2) )/(5^(2) ) - (y^(2) )/(4^(2) ) =1`

Notice that the negative variable is
`y`, that means the hyperbola is horizontal. Also, its focal poitns are on the x-axis and have the form
`(c,0)` and
`(-c,0)`.

Remember that the parameter
`a` is always with the positive varible. So,

`a^(2)=5^(2) \implies a=5`

`b^(2)=4^(2) \implies b=4`

The asymptotes are

`y=-(b)/(a)x` and
`y=(b)/(a)x`, replacing parameters, we have

`y=-(4)/(5)x` and
`y=(4)/(5)x`

So, the hyperbola is shown in the image attached, there you can observe that the vertices are
`(-5,0)` and
`(5,0)`, which matches the parameter
`a`.