Answer:
The center of the hyperbola is (-5 , 7)
The left vertex is (-5 , -6)
The other vertex is (-5 , 20)
Explanation:
* Lets explain the equations 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
- The hyperbola is open horizontally
- The coordinates of the vertices are (h ± a , k)
- 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 hyperbola is open vertically
- The coordinates of the vertices are (h , k ± a)
* Lets solve the problem
∵ The equation of the hyperbola is - (x + 5)²/9² + (y - 7)²/13² = 1
- Lets rearrange the terms of the equation
∴ The equation is (y - 7)²/13² - (x + 5)²/9² = 1
∴ The hyperbola opens vertically
∵ (y - k)²/a² - (x - h)²/b² = 1
∴ a = 13 , b = 9 , h = -5 , k = 7
∵ The coordinates of its center are (h , k)
∴ The center of the hyperbola is (-5 , 7)
∵ The hyperbola opens vertically
∴ Its vertices are (h , k - a) the bottom one and (h , k + a) the up one
∴ The bottom vertex is (-5 , 7 - 13) = (-5 , -6)
∴ The bottom vertex is (-5 , -6)
∴ The other vertex is (-5 , 7 + 13) = (-5 , 20)
∴ The other vertex is (-5 , 20)