Find an equation for the hyperbola described Graph she equat

Find an equation for the hyperbola described Graph she equation Foci at (6.9) and (10.9); vertex at (9.9) Write an equation for the hyperbola. - = 1 (Type exact answers for each term, using fractions as needed.) Select the graph which correctly describes the hyperbola.

Solution

Focii (6,9),(10,9)focii=(h+-c,k)

Therefore k=9

h+c=10, h-c=6

h=8, c=2

vertex (9,9)

(h+a,k)

h+a=9

a=1

b^2=c^2-a^2=4-1=3

(x-8)^/1 -(y-9)^/3 =1