Lesson 3: 9.3 Hyperbolas and Rotation of Conics

How do you solve problems involving hyperbolas, classify a conic from its general equation, and eliminate the xy-term from the general equation of a conic section?

hyperbola
branches
transverse axis
asymptotes

HSG.GPE.A.3 - Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

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Real-life problems involving satellite signals and the speed of sound can be solved using hyperbolas, the final conic section to study in this chapter.

Hyperbolas can be used to model and solve many types of real-life problems. For example, they can be used to locate the position of an explosion that was recorded by three listening stations.

Students may incorrectly graph the branches of a hyperbola through the asymptotes. Remind students that the branches approach the asymptotes, but never intersect them.

Students learning English may have difficulty recalling which conic section is a parabola and which is a hyperbola. Tell them that the prefix hyper- means "over and above". Help them use this definition to recall that a hyperbola forms two curves on a graph. Two curves are "over and above" the one curve of a parabola.

Use Common Assessments

Pre-Calculus with Limits