Answer:
- 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)
