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High school mathematics: ellipse
The vertices of the ellipse x 2/4+y 2/3 =1are (soil 2,0), (0, soil √3) respectively.

In order to solve the elliptic standard equation, there are two cases in which two points are selected as the focus from these four points:

1) focusing on (soil 2,0), c=2,

2a=√ 13+√5,a=(√ 13+√5)/2,

b^2=a^2-c^2=(9+√65)/2-4=( 1+√65)/2,

The standard equation of ellipse is x 2/[(9+√ 65)/2]+y 2/[(1+√ 65)/2] =1.

2) Focus on (0, soil √3), c=√3,

2a=√(8+4√3)+√(8-4√3),a=√(2+√3)+√(2-√3),

a^2=6,b^2=a^2-c^2=3,

The standard equation of ellipse is y 2/6+x 2/3 =1.