x2/100-y2/144=1 is a hyperbola.
Asymptotes are found from:
x2/100=y2/144,
x/10=±y/12,
x/5=±y/6, y=6x/5 and y=-6x/5 are the asymptotes.
The vertices are (-10,0) and (10,0), because y2/144=x2/100-1, so y can only exist when |x|≥10, that is, when x≤-10 or x≥10.