How do you find the equation of a ellipse when given coordinates where the graph passes through?

Ex) Find the equation with center at the origin, vertex at (0,4) and passes through (√3, 2√3)?

EDIT: Found out I plugged in the A value (16 in this problem) in the wrong spot, making X some weird fraction. My next question is, how do you figure out what the major axis is in this equation, when they don't give the foci coordinates?