[ Interactive: Hyperbolas ]To easily graph the asymptotes of a hyperbola use the following process.
Step 1: Identify the center (h, k) from standard form.
Step 2: Plot points a units left and right from center.
Step 3: Plot points b units up and down from center.
Step 4: Draw the rectangle defined by these points.
Step 5: The lines though the corners of this rectangle are the asymptotes!
Graph the hyperbola, x- and y- intercepts, and give the equations of the asymptotes.
Example: Find the equation of the hyperbola centered at (-3, 1) where a = 2, b = 3, and with a vertical transverse axis. Graph it.