Question

What are the equations of the asymptotes of the hyperbola? (y+4)236−(x−6)249=1 enter your answer in point-slope form by filling in the boxes. Enter the slope as a simplified fraction.

Answer 1

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