Question

Find the equation of the hyperbola whose vertices are at (-1,-5) and
(-1,1) with a focus at (-1,-7). Please and thank you.

Answer 1

centre must be the midpoint of the vertices
centre is (-1, -2)
after making a sketch we can see the major axis is vertical and
a = 3, c = 5
a^2 + b^2 = c^2
9+b^2 = 25
b^2 = 16

(x+1)^2 /6 - (y+2)^2 /9 = -1

Answer 2

Thank you so much!