Question

Find the slopes of the asymptotes for the hyperbola.

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

Answer 1

General equation is given be

`\boxed{\sf (y^2)/(a^2)-(x^2)/(b^2)=1}`

On comparing

• a^2=81=>a=9
• b^2=144=>b=12

Now

`\\ \rm\Rrightarrow m=\pm (a)/(b)=\pm(9)/(12)=\pm (3)/(4)`

Option A is correct

Answer 2

• A. m = 3/4 and m = -3/4

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