Determine if the transverse axis is horizontal or vertical for the following hyperbolas.
$\frac{y^2}{9}-\frac{x^2}{9}=1$

• A. Horizontal
• B. Vertical
• C. Cannot be determined

Answer: (B)

Verified step by step guidance

1. Identify the standard form of the hyperbola equation. It is given as \(\frac{y^2}{9} - \frac{x^2}{9} = 1\).
2. Recall that for hyperbolas, if the \(y^2\) term is positive and comes first, the transverse axis is vertical. Conversely, if the \(x^2\) term is positive and comes first, the transverse axis is horizontal.
3. In this equation, the positive term is \(\frac{y^2}{9}\), which indicates the transverse axis is vertical.
4. The denominators under \(y^2\) and \(x^2\) represent \(a^2\) and \(b^2\) respectively, where \(a^2 = 9\) and \(b^2 = 9\) in this case.
5. Therefore, since the \(y^2\) term is positive and first, the transverse axis is vertical.