The ellipse has its centre at the origin (0,0) because of the symmetry of its foci and vertices.
The foci lie on the x axis so it’s a horizontal ellipse with standard equation x²/a²+y²/b²=1 where a and b are the lengths of the semi major and semi minor axes respectively. The y intercepts are when x=0 so y²/b²=1 and b²=y²=9 because 3 and -3 squared are both 9. c²=a²-b² where c is the distance of each focus from the centre. We know this distance is 4, so 16=a²-9, and a²=25. So the equation is x²/25+y²/9=1.
This can be written 9x²+25y²=225.