8. Graph x² - y² = 4

This is an hyperbola centered at the origin which crosses the x axis.If we divide both sides by 4, we rewrite as

which is in the form

where the x intercepts will be at plus or minus a, and the asymptotes will be lines through the origin whose slopes are plus or minus b/a. Since and and b are both 2, the x intercepts are at plus and minus 2, and the asymptotes are the lines through the origin at 45^o angles.