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The question asks, "Which of the following equations describes a hyperbola?"

### Let's analyze the options:
1. \( x^2 + y^2 = 1 \): This is the equation of a **circle**.
2. \( x^2 - y^2 = 1 \): This is the equation of a **hyperbola**.
3. \( \frac{x^2}{5} + \frac{y^2}{12} = 1 \): This is the equation of an **ellipse**.
4. \( \frac{x^2}{5} - \frac{y^2}{12} = 1 \): This is the equation of a **hyperbola**.

### Correct answers:
- \( x^2 - y^2 = 1 \)
- \( \frac{x^2}{5} - \frac{y^2}{12} = 1 \)

Both equations describe a hyperbola, with the second one representing a stretched hyperbola.

Do you want further details or have any questions?

Here are some related questions for deeper understanding:
1. What are the standard forms of a hyperbola's equation?
2. How do you distinguish between ellipses and hyperbolas?
3. What are the characteristics of a hyperbola's asymptotes?
4. How do you find the foci of a hyperbola?
5. What is the difference between a vertical and horizontal hyperbola?

**Tip:** Hyperbolas have subtraction in their equations, while ellipses involve addition.

Which of the following equations describes a hyperbola?

Learn how to identify hyperbolas from various conic section equations. Understand the difference between circles, ellipses, and hyperbolas, and explore their respective formulas. This problem is suitable for high school students learning conic sections.

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