Answer:
The foci are (2 , 7) and (2 , -3)
Explanation:
* lets revise the equation of the hyperbola
- The standard form of the equation of a 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 ± a , k )
- The coordinates of the co-vertices are ( h , k ± b )
- The coordinates of the foci are (h , k ± c), where c² = a² + b²
* Now lets solve the problem
∵ The equation of the hyperbola of vertex (h , k) is
(y - k)²/a² - (x - h)²/b² = 1
∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1
∴ k = 2 , h = 2 , a = 3 , b = 4
∵ The foci of it are (h , k + c) and (h , k - c)
- Lets find c from the equation c² = a² + b²
∵ a = 3
∴ a² = 3² = 9
∵ b = 4
∴ b² = 4² = 16
∴ c² = 9 + 16 = 25
∴ c = √25 = 5
- Lets find the foci
∵ The foci are (h , k + c) and (h , k - c)
∵ h = 2 , k = 2 , c = 5
∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)
∴ The foci are (2 , 7) and (2 , -3)