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. Recall the standard form of a hyperbola equation: for a horizontal transverse axis, it is \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), and for a vertical transverse axis, it is \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\).
2. Compare the given equation \(\frac{y^2}{9} - \frac{x^2}{9} = 1\) to the standard forms to identify which variable's term is positive and which is negative.
3. Notice that the \(y^2\) term is positive and the \(x^2\) term is negative, matching the form \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\).
4. Since the positive term corresponds to \(y^2\), the transverse axis is vertical (along the y-axis).
5. Conclude that the hyperbola has a vertical transverse axis based on the position of the positive term in the equation.