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. Identify the standard form of the hyperbola equation, which is either \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\).
2. Look at the given equation: \(\frac{x^2}{12} - \frac{y^2}{16} = 1\). Notice that the \(x^2\) term is positive and comes first, while the \(y^2\) term is subtracted.
3. Recall that if the \(x^2\) term is positive and comes first, the transverse axis is horizontal. Conversely, if the \(y^2\) term is positive and comes first, the transverse axis is vertical.
4. Since the \(x^2\) term is positive and first in the equation, conclude that the transverse axis is horizontal.
5. Therefore, the hyperbola opens left and right along the horizontal axis.