Find the equations of the asymptotes of the hyperbola defined by the equation shown below. If necessary, round to the nearest tenth.

Question

−64x^2+ 9y^2- 1024x + 144y-4096 = 0
Asymptotes: =
and y=

Answer 1

The equation can be written as
(y+8)^2/64 - (x+8)^2/9 = 1
which gives us
b = 8, a = 3
making the asymptotes y+8 = ±8/3 (x+8)

Answer 2

Simplifying, we get the equations of the asymptotes as:

y = (8/3)x - 32/3 and y = -(8/3)x - 56/3

Rounded to the nearest tenth:

y = 2.7x - 10.7 and y = -2.7x - 18.7