Judging from the meaning of the question, b=c= radical number 2, then A 2 = B 2+C 2 = 4.

So the elliptic equation is x 2/4+y 2/2 =1.

2.

The elliptic equation is: x 2/4+y 2/2 = 1,

c=√2，

The right focus f (√ 2,0), that is, there is p/2= root number 2, then there is a parabolic equation that is y 2 = 2px = root number 2x.

Let A(x 1, y 1), B(x2, y2),

Equation AB: y=x+m, or x-y+m=0,

Substituting the linear equation into the parabolic equation,

X 2+(2m-4 radical number 2) X+M 2 = 0

According to Vieta's theorem,

X 1+x2= 4 root number 2-2m

x 1*x2=m^2

According to the chord length formula,

|ab|=√( 1+ 1^2)[x 1-x2)^2

=√2*[(x 1+x2)^2-4x 1x2]

=√2[32- 16 root 2m+4m 2-4m 2]

=4√(4-2 root number 2m),

Distance from right focus F to AB h=|√2-0+m|/√2

= 1+|m|/√2，

S △ ABF = | AB | * h/2 = 2 (1+| m |/√ 2) √ (4-2 2m)