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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.

Which shape is defined by the equation x^2/4 - y^2/9 = 1?

This article explores how to identify a hyperbola based on its equation x^2/4 - y^2/9 = 1. Learn about the standard form of a hyperbola and how to differentiate it from other conic sections. Suitable for students in Grades 10-12.

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