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Home Limits, Analytic Geometry, and Approximations Ellipses and Hyperbolas Theorem 2
 
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Theorem 2

THEOREM 2

For any positive a and b, the graph of the equation

05_limits_g_approx-312.gif

is a hyperbola with its center at the origin. Its transverse axis is the y-axis, and its conjugate axis is the x-axis. The vertices are at (0, ±b), and the foci are at (0, ±c), where c is found by

a2 + b2 = c2.

The graph of the equation

05_limits_g_approx-313.gif

is a hyperbola with similar properties with the roles of x, a and y, b reversed. The proof of Theorem 2 uses a computation like the proof of Theorem 1 on ellipses and is omitted.
Home Limits, Analytic Geometry, and Approximations Ellipses and Hyperbolas Theorem 2

Last Update: 2006-11-05