Question

Which graph represents the hyperbola? x^2/5^2 - y^2/4^2 = 1

Answer 1

Answer:

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

Step-by-step explanation:

The given formula is

$\frac{x^{2} }{5^{2} } - \frac{y^{2} }{4^{2} } =1$

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

$y=-\frac{b}{a}x$ and $y=\frac{b}{a}x$, replacing parameters, we have

$y=-\frac{4}{5}x$ and $y=\frac{4}{5}x$

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 $a$.