D: 5Y？ +2√3Y- 1=0

y=(-√3+2√2)/5，y=(-√3-2√2)/5

y 1-y2=4√2/5

Because in the ellipse X 2+4Y 2-4 = 0, A = 2, B = 1 and C = √ 3.

X=y+√3 passes through the focus f (√ 3,0) of the ellipse.

S△AOB=S△AOF+S△FOB

= 1/2 *(y 1-Y2)√3 = 1/2 * 4√2/5 *√3 = 2√6/5