Question

PLEASEE HELP!!

The equation of a hyperbola is .
The equations of the asymptotes of the hyperbola are and .

Answer 1

Answer: I just did this quiz in Plato the correct answer is in the pic I did this question 3 times because I listened to the other people and finally got the answer which is the correct one, Hope this helps :)

Explanation:

Answer 2

y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Explanation:

* Lets revise the equation of the hyperbola with center (h , k) and

transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are (h , k ± a)

- The coordinates of the co-vertices are (h ± b , k)

- The coordinates of the foci are (h , k ± c) where c² = a² + b²

- The equations of the asymptotes are ± a/b (x - h) + k

* Lets solve the problem

∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1

∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1

∴ h = -2 , k = 2

∴ a² = 9

∴ a = √9 = 3

∴ b² = 1

∴ b = √1 = 1

∵ The equations of the asymptotes are y = ± a/b (x - h) + k

∴ The equations of the asymptotes are y = ± 3/1 (x - -2) + 2

∴ The equations of the asymptotes are y = ± 3 (x + 2) + 2

* The equations of the asymptotes of the hyperbola are

y = 3(x + 2) + 2 and y = -3(x + 2) + 2