type the correct answer in each box. write coordinate points in the form (x, y).
consider the hyperbola represented by the equation .
the center of this 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 the hyperbola is (-5 , 7)

The left vertex is (-5 , -6)

The other vertex is (-5 , 20)

Step-by-step 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)