The two branches of the graph of a hyperbola approach a pair of intersecting lines, called​ _____. These intersecting lines pass through the​ _____ of the hyperbola.

Group of answer choices

center; asymptotes

origin; vertical lines

vertical lines; origin

asymptotes; center

The correct answer is:

**asymptotes; center**

Explanation: 
The two branches of a hyperbola approach two intersecting lines called **asymptotes**. These asymptotes pass through the **center** of the hyperbola. The asymptotes provide a guideline for how the branches of the hyperbola behave as they extend towards infinity.

Would you like more details on hyperbolas or any other aspect of this topic?

Here are 5 related questions to explore:
1. What is the standard equation of a hyperbola centered at the origin?
2. How do you find the equations of the asymptotes for a hyperbola?
3. What is the difference between a hyperbola's transverse axis and conjugate axis?
4. How do the asymptotes differ for horizontal and vertical hyperbolas?
5. How can the eccentricity of a hyperbola be calculated?

**Tip:** The slopes of the asymptotes for a hyperbola can be derived from the equation, and their values depend on the orientation of the hyperbola.

The two branches of the graph of a hyperbola approach a pair of intersecting lines, called _____. These intersecting lines pass through the _____ of the hyperbola.

Explore the key concepts of hyperbolas in analytic geometry. Learn about the intersecting lines known as asymptotes, which pass through the center of the hyperbola. Understand the standard equations, asymptotes, and their relationship to the hyperbola's graph. Suitable for high school students in Grades 10-12.

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