How is the difference | L1 L2 | related to the values of a and/or b? (Hint: Think about multiples.) Determine the difference | L1 L2 | for a hyperbola where a = 3 and b = 4. Observe the values of L1, L2, and the difference | L1 L2 | as you vary the values of a and b. Do the lengths of L1 and L2 change? What do you notice about the absolute value of the differences of the lengths? How do these observations relate to the geometric definition of a hyperbola. Drag the purple point around the hyperbola. A purple point will appear on the hyperbola, along with two line segments labeled L1 and L2. Conic SectionsHyperbolasDefinitionThe conic section formed by a plane which intersects both of the right conical surfacesFormed when or when the plane is parallel to the axis of the cone DefinitionA hyperbola is the set of all points in the plane whereThe difference between the distancesFrom two fixed points (foci)Is a constantGeogebraDemonstrationExperimenting with DefinitionTurn on Explore geometric definition.
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