Question 1082607
let (x-h)^2/a^2 + (y-k)^2/b^2 = 1. the general equation.

we have to solve the system:

1) (1-h)^2/a^2 + (2+k)^2/b^2 = 1
2) h^2/a^2 + (1-k)^2/b^2 =1
3) (1+h)^2/(a^2) + (2+k)^2/b^2 = 1
4) h^2/a^2 + (5+k)^2/b^2 = 1

3) - 1) 4h/a^2 =0 so h = 0.

4) - 2) (24 + 12k)/b^2 = 0, so k =-2.

replacing on 1) 1/a^2 = 1, so a^2 = 1.

replacing on 2) 9/b^2 = 1, so b^2 = 9.

Answer: x^2 + (y+2)^2/9 = 1 

@natolino_