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.
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:
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.
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.