Algebra and Trigonometry, 5th Edition

10.3 The Hyperbola

• Given an equation of a hyperbola, complete the square, if necessary, and then find the center, the vertices, and the foci and graph the hyperbola.

The last type of conic section that we will study is the hyperbola.

Hyperbola

A hyperbola is the set of all points in a plane for which the absolute value of the difference of the distances from two fixed points (the foci) is constant. The midpoint of the segment between the foci is the center of the hyperbola.

Standard Equations of Hyperbolas

We first consider the equation of a hyperbola with center at the origin. In the figure at left, $F_1$ and $F_2$ are the foci. The segment ...