The centre of the ellipse is at the origin because the foci are equidistant from the origin and lie on the y axis.
The general equation of such an ellipse is x²/a²+y²/b²=1 or x²/b²+y²/a²=1. The ellipse is vertical because the foci are on the y axis. That means we take the second standard form of the ellipse, where a is the length of the semi major axis and b the length of the semi minor axis. The co-vertices are on the x axis and lie on the ellipse itself. We can plug in the coords: 1/b²=1 so b=1. c²=a²-b² where c is the distance of either focus from the centre of the ellipse, which in this case is (0,0). Therefore, since c=3, 9=a²-b²=a²-1, and a²=10.
The equation of the ellipse is x²+y²/10=1. This looks better if we multiply through by 10: 10x²+y²=10.