Question

Find the slopes of the asymptotes for the hyperbola.

y^2/81 - x^2/144=1

Answer 1

Answer:

• A. m = 3/4 and m = -3/4

Step-by-step explanation:

According to hyperbola form:

• y²/a² - x²/b² = 1

The slope of the asymptote is:

• m = ± a/b, since the hyperbola is vertical

Find the slope:

• m = ± √81/√144= ± 9/12 = ± 3/4

Correct choice is A

Answer 2

General equation is given be

$\boxed{\sf \dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1}$

On comparing

• a^2=81=>a=9
• b^2=144=>b=12

Now

$\\ \rm\Rrightarrow m=\pm \dfrac{a}{b}=\pm\dfrac{9}{12}=\pm \dfrac{3}{4}$

Option A is correct