Identify the vertices and asymptotes of each. X^2/100-y^2/144=1

Question

X^2/100-y^2/144=1

Answer 1

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.