Basic Technical Mathematics, 11th Edition

21.6 The Hyperbola

• Foci • Vertices • Asymptotes • Transverse Axis • Conjugate Axis • Standard Equation–Axis along x-axis • Standard Equation–Axis along y-axis • Calculator Display • $xy\hspace{0.17em}=\hspace{0.17em}\text{c}$ Hyperbola

A hyperbola is defined as the locus of a point P(x, y) that moves so that the difference of the distances from two fixed points (the foci) is constant. We choose the foci to be $(\hspace{0.17em}-\hspace{0.17em}c\hspace{0.17em},\hspace{0.17em}0)$ and (c, 0) (see Fig. 21.69), and the constant difference to be 2a. As with the ellipse, c is the length of the line segment from the center to a focus, and a (as we will see) the length of the line segment from the center to a vertex. Therefore,

Fig. 21.69 ...