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. Start by examining the given equation: \(\frac{x^2}{4} - \frac{y^2}{9} = 1\).
2. Recall the general forms of conic sections: an ellipse has the form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) where both terms are added, while 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.
3. Notice that in the given equation, the \(x^2\) term divided by 4 and the \(y^2\) term divided by 9 are separated by a minus sign, indicating subtraction.
4. Since the equation matches the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), this identifies the conic as a hyperbola.
5. Therefore, based on the structure of the equation and the signs between the terms, conclude that the equation represents a hyperbola.