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 bottom vertex is ( -5, 7 - 5 sqrt(10)). The other vertex is ( -5, 7 + 5 sqrt(10))

Step-by-step explanation:

The equation of the hyperbola is:

-(x+5)^2/9^2+(y-7)^2/13^2=1

This is the same that:

(y-7)^2/13^2-(x+5)^2/9^2=1

This equation has the form:

(y-k)^2/a^2-(x-h)^2/b^2=1

and the hyperbola opens vertically, then the coordinates of the bottom vertex are: (h,k-c). The other vertex is (h,k+c)

Comparing with the form:

-h=5→h=-5

k=7

a^2=13^2

b^2=9^2

c^2=a^2+b^2→c^2=13^2+9^2→c^2=169+81→c^2=250→sqrt(c^2)=sqrt(250)→

c=sqrt(25*10)→c=sqrt(25) sqrt(10)→c=5 sqrt(10)

The bottom vertex is: (h,k-c)=(-5, 7 - 5 sqrt(10))

The other vertex is: (h,k+c)=(-5, 7 + 5 sqrt(10))