Hyperbola: Asymptote

The asymptote is a line
the graph follows.

So, for a hyperbola,
there are two asymptotes.

Hyperbola: Equation

For the horizontal hyperbola
x²/a² - y²/b² = 1,

the asymptotes are
y = ±[b/a]x.

9 = 3²
16 = 4²

x²/3² - y²/4² = 1

a = 3
b = 4

Then the asymptotes are
y = ±[4/3]x.

So y = ±[4/3]x is the answer.

For the vertical hyperbola
y²/a² - x²/b² = 1,

the asymptotes are
y = ±[a/b]x.

a and b are switched.

To make the right side 1,
divide both sides by 9.

9 = 3²

-x²
= -x²/1
= -x²/1²

y²/3² - x²/1² = 1

a = 3
b = 1

Then the asymptotes are
y = ±[3/1]x.

√x

3/1 = 3

So y = ±3x is the answer.