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

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

2 answers

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)
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
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