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(b) Find the equation of the hyperbola with vertices (±3, 0) and eccentricity e = 2.
(c) With the help of your classmates, ﬁnd the eccentricity of each of the hyperbolas in
number 1. What role does eccentricity play in the shape of the graphs?
8. With the help of your classmates, research the shape of cooling towers for nuclear power
plants and other ways hyperbolas have been used in architecture and design.
9. With the help of your classmates, research the Cassegrain Telescope. It uses the reﬂective
property of the hyperbola as well as that of the parabola to make an ingenious telescope.
10. With the help of your classmates show that if Ax2 + Cy 2 + Dx + Ey + F = 0 determines a
non-degenerate conic5 then
• AC < 0 means that the graph is a hyperbola
• AC = 0 means that the graph is a parabola
• AC > 0 means that the graph is an ellipse or circle
NOTE: This result will be generalized in Theorem 11.11 in Section 11.6.1. 3
Back in the Exercises in Section 1.1 you were asked to research people who believe the worl...
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