The given equation is:

$\frac{x^2}{4} - \frac{y^2}{9} = 1$

This is a standard form of the equation of a hyperbola. The general form of a hyperbola is:

$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$

where $a^2$ and $b^2$ are the denominators of the $x^2$ and $y^2$ terms, respectively. In this case:

• $a^2 = 4$, so $a = 2$,
• $b^2 = 9$, so $b = 3$.

Since the equation has a subtraction sign between the two terms, and the $x^2$ term comes first, it represents a horizontal hyperbola.

Thus, the correct answer is Hyperbola.

Would you like more details on how to differentiate between conic sections?

Here are 5 related questions:

1. How can you identify a circle from its equation?
2. What is the difference between the equations of an ellipse and a hyperbola?
3. What are the foci of a hyperbola, and how are they calculated?
4. How does the orientation of a hyperbola change based on the equation?
5. What real-life applications involve hyperbolas?

Tip: The signs between the squared terms in conic section equations help determine whether the shape is a circle, ellipse, parabola, or hyperbola.