The following questions are setup as challenges to the student:
1. Suppose l and m are intersecting lines and m is rotated around l to form a cone. Now a plane P intersects the cone.
Which position of P gives a hyperbola?
Which position of P gives an ellipse?
Which position of P gives a parabola?
Check the graphs presented below:
P parallel to m:
P parallel to l: 
P perpendicular to l: 
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2. Graph
Write several sentences comparing and contrasting the graphs. e.g. similarities: reflections, shape, length of the focal constant, asymptotes; differences: axis they lie on.
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3. Consider the hyperbola:
Find the coordinates of six points on the graph.
Give the equations for its asymptotes.
Use the results of the coordinates to determine which of the following is a reasonable graph of the hyperbola.
A.
B.
C.
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4. Compare the graphs of the following two hyperbolas:
How are these two graphs related?
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