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?

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?

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