Unformatted text preview: the asymptotes (the center of the hyperbola). Suppose we want to move one of these loci to a new location: that is, we want to displace the locus (without rotation) so that the special point given by the origin for the model equation moves to ( α,β ). Any such motion is accomplished by replacing x with x plus a constant and y with y plus another constant inside the equation; we need to do this in such a way that substituting x = α and y = β into the new equation leads to the same calculation as substituting x = 0 and y = 0 into the old equation. It may seem wrong that this requires replacing x with x − α and y with y − β in the old equation; to convince ourselves that it is right, let us consider a few...
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 Fall '08
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 Calculus, Equations, Asymptotes, Conic section

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