## Hyperbolas.jpeg - Section 1: Launch

# Hashing Out Hyperbolas

Lesson 3 of 10

## Objective: SWBAT solve problems using hyperbolas.

#### Launch

*10 min*

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.

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#### Explore

*15 min*

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.

#### Resources

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#### Summarize

*25 min*

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.

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Conics Sections with Princess the Dog
- LESSON 2: Exploring Ellipses
- LESSON 3: Hashing Out Hyperbolas
- LESSON 4: Pondering Parabolas
- LESSON 5: Classifying Conics
- LESSON 6: Rotated Conic Sections - Day 1 of 2
- LESSON 7: Rotated Conic Sections - Day 2 of 2
- LESSON 8: Unit Review: Conic Sections
- LESSON 9: Review Game: Lingo
- LESSON 10: Unit Assessment: Conic Sections