# Hashing Out Hyperbolas

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## Objective

SWBAT solve problems using hyperbolas.

#### Big Idea

Analyze hyperbolas using three different lenses.

## Launch

10 minutes

Like yesterday, I start class by having students think about the three different ways that we can define a hyperbola (slide #2 of the PowerPoint). I refer them back to the poster they made if they are unsure of any of these.

I find that my students are unsure how to define a hyperbola as a locus. This is something I have to tell them or I have them look in their book. Comparing it to an ellipse is also helpful, instead of the sum of the distances to the foci being a constant, the difference of the distances is constant.

## Explore

15 minutes

On slide #3 of the PowerPoint, I give students an equation of a hyperbola and have them graph it with their table while also thinking about some of the features of the graph (asymptotes, eccentricity, etc.). I will give them about 10 minutes to work on this with their table groups. As they are working I will go around the room and make sure they are on the right track. Here are some questions I will ask to gauge their understanding:

• How do you know if this hyperbola is horizontal or vertical?
• What is the name of the line of symmetry of the hyperbola?
• What does the a value represent? The b value?
• What equation represents a, b, and c?

After they have had sufficient time to work, we will regroup and I will ask a student to share their work. If I feel it is necessary, we will discuss some of the questions that I asked while students were working.

Finding the asymptotes is usually challenging for my students. I discuss more about these in the video below.

## Summarize

25 minutes

Finally, I will give students some homework problems from our textbook to summarize hyperbolas. I make sure that there are writing equations or graphing problems given a variety of information. For example, finding the equation given the center and asymptotes, or given the foci and vertices.