Determine if the transverse axis is horizontal or vertical for the following hyperbolas.
$\frac{x^2}{12}-\frac{y^2}{16}=1$

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

Answer: (A)

Verified step by step guidance

1. Recall that the standard form of a hyperbola is either \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\), where \(a^2\) and \(b^2\) are positive constants.
2. Identify which variable's term is positive and which is negative in the given equation \(\frac{x^2}{12} - \frac{y^2}{16} = 1\).
3. Since the \(x^2\) term is positive and the \(y^2\) term is subtracted, this matches the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\).
4. For hyperbolas in this form, the transverse axis is along the \(x\)-axis, meaning it is horizontal.
5. Therefore, conclude that the transverse axis of the given hyperbola is horizontal.