Hyperbolas

Example 1

Graph the following hyperbola. Find its center, vertices, foci, and the equations of its asymptote lines.

Step 1. Identify the center, vertices, foci, and the equations of asymptotes.

This is a hyperbola with center at (0, 0), and its transverse axis is along the x-axis.

Vertices: (-4, 0), (4, 0)

Foci: (?41, 0), (-?41, 0)

Equations of asymptote lines:

Step 2 . Graph the conic.