finding equation of an ellipse

Question

I was given the pionts (2,0) (-2,0) (0,3) (0,-3) and i have to fins the equation. 

Answer 1

When plotting the points, it is clear that the major axis for this ellipse is the x-axis.
It is also clear that the center is (0,0)

The base equation for and ellipse with x axis major, and center at the origin is

x²/a² + y²/b² = 1

a = distance from center to a major axis vertex. The distance from the origin to (0,3), is 3
a = 3

b = distance from center to a minor axis vertex. The distance fro the origin to (2,0), is 2
b = 2

Thus, the equation of the ellipse is:

x²/3²+ y²/2² = 1