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Unformatted text preview: y/x = b/a . It is straightforward to check that as a point P ( x,y ) moves along the hyperbola with x , the ratio y/x tends to b/a , so the distance of P from one of these lines goes to zero. These lines are called the asymptotes of the hyperbola. The distance from the origin to the two foci is given by the formula c =  ae  = R a 2 + b 2 A consequence of this formula is another characterization of a a hyperbola (Exercise 9 ): The (absolute value of the) diFerence between the distances of any point on the hyperbola to the two foci equals the transverse axis. This information is illustrated in Figure 2.8 ....
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 Fall '08
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 Calculus, Conic Sections

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