Hyperbolas
What is a hyperbola? The word hyperbola comes from a greek word meaning excess or extravagance because it's curvature is very different from that a circle (moreso than a parabola or an ellipse). The hyperbola can be generated by a function whose equation is of the form y=a/x where a is any fixed number and x is a variable.
The Hyperbola Emerges
Let's take a look at the graph y=1/x, shown below
1. Describe the shape of this hyperbola.
2. What happens if y=0 or x=0 in the equation? How might this relate to the graph?
3. Why does this graph have two "sections"?
4. What do you think the graph of y=-1/x would look like?
Activity: Class Discussion on these questions
The Inverse Relationship
Perhaps this graph looks strangely familiar. This graph is also the graph for an inverse kind of indirect, or negative relationship.
1. What happens to pressure as temperature increases? What does this say about the relation of a hyperbola?
Activity: Class Discussion
What is the relationship between temperature and pressure in this picture?
Reflection
What have you learned about hyperbolas in real world contexts? What is the relation of a hyperbola?