Determine if the transverse axis is horizontal or vertical for the following hyperbolas.
$3x^2-y^2=18$

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

Answer: (A)

Verified step by step guidance

1. Start with the given equation of the hyperbola: \$3x^2 - y^2 = 18$.
2. Rewrite the equation in standard form by dividing every term by 18 to isolate 1 on the right side: \(\frac{3x^2}{18} - \frac{y^2}{18} = 1\).
3. Simplify the fractions to get: \(\frac{x^2}{6} - \frac{y^2}{18} = 1\).
4. Identify the terms: since the \(x^2\) term is positive and comes first, and the \(y^2\) term is subtracted, this matches the standard form of a hyperbola with a horizontal transverse axis: \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\).
5. Therefore, the transverse axis is horizontal because the positive term is associated with \(x^2\).