Question

find the vertices of the hyperbola. enter the smallest x coordinate first.
$\frac{x^{2}}{9}-\frac{y^{2}}{49}=1$
(?, ) and (, )

Explanation:

Step1: Recall hyperbola standard form

The standard form of a hyperbola is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1$, and its vertices are $(\pm a,0)$.

Step2: Identify the value of a

For the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{49}=1$, we have $a^{2}=9$, so $a = 3$.

Answer:

$(-3,0)$ and $(3,0)$