12.4 Hyperbolas
Unit 12 · Conic sections
Ideas in this lesson
Centers and transverse axes
The positive squared term identifies the direction of the transverse axis.
Hyperbola vertices
The vertices lie on the transverse axis one transverse semiaxis from the center.
Vertices and foci
For a hyperbola, the squared focal distance equals the sum of the squared semiaxis parameters.
Asymptotes
The asymptote slopes come from the horizontal and vertical semiaxis lengths in the standard equation.
Write a hyperbola equation
Choose the sign order from the transverse axis, then use the squared parameters as denominators.
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