Consider the hyperbola represented by the equation: (picture)

the center of the hyperbola is

the left vertex, if the hyperbola opens horizontally, or the bottom vertex, if it opens vertically, is

the other vertex is

- The center of hyperbola is (-2 , 3)

- The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

- The other vertex is (2 , 3)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1, Where

- The length of the transverse axis is 2a

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

- The length of the conjugate axis is 2b

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

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

* Now lets solve the problem

∵ (x + 2)²/4² - (y - 3)²/5² = 1

∵  (x - h)²/a² - (y - k)²/b² = 1

∴ a = 4 , b = 5

∴ h = -2 , k = 3

∵ The center of the hyperbola is (h , k)

∴ The center of hyperbola is (-2 , 3)

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

∴ The coordinates of the vertices are (-2 + 4 , 3)  , (-2 - 4 , 3)

∴ The coordinates of the vertices are (2 , 3)  , (-6 , 3)

∴ The left vertex, if the hyperbola opens horizontally, or the

  bottom vertex, if it opens vertically, is (-6 , 3)

∴ The other vertex is (2 , 3)