The point slope form of the asymptote of the hyperbola is; y - 4 = ±(6/7)(x - 6)
- We are given the equation of the hyperbola as;
[(y + 4)²/36] - [(x - 6)²/49] = 1
- We can rewrite this equation as;
[(y + 1)²/6²] - [(x - 6)²/7²] = 1
- The general equation form of hyperbola is;
[(y - k)²/a²] - [(x - h)²/b²] = 1
- Comparing this general form to our given equation we can see that;
k = -4
h = 6
a = 6
b = 7
- Now the equation of the asymptote of a hyperbola follows the general formula;
y = ±[a(x - h)/b] + k
- Plugging in the relevant values gives us;
y = ±(6/7)(x - 6) - 4
>> y - 4 = ±(6/7)(x - 6)
Read more about hyperbola asymptotes at; brainly.com/question/12919612
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