Identify whether the equation is of an ellipse or hyperbola.
$\frac{x^2}{4}-\frac{y^2}{9}=1$

• A. Ellipse
• B. Hyperbola
• C. Neither of the above

Answer: (B)

Verified step by step guidance

1. Recall the general forms of the equations for ellipses and hyperbolas. An ellipse has the form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where both terms are added.
2. A hyperbola has the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where one term is subtracted from the other.
3. Look at the given equation: \(\frac{x^2}{4} - \frac{y^2}{9} = 1\). Notice the subtraction sign between the two fractions.
4. Since the equation has a subtraction between the squared terms and equals 1, it matches the general form of a hyperbola.
5. Therefore, based on the structure of the equation, you can identify it as the equation of a hyperbola.