∴a=2==>； c=a/2= 1== >b^2=4- 1=3

The elliptic equation is x 2/4+y 2/3 =1.

(2) Analysis: ∵ The inclination of the line passing through the right focus F is 45 degrees, and the intersecting ellipse is in A and B..

P is a point on an ellipse and satisfies the vector OP=λ(OA+OB).

F( 1，0)

The straight line is y = x-1= > y 2 = x 2-2x+1

7x 2-8x-8 = 0 = = > x 1 =(4-6√2)/7，x2=(4+6√2)/7

∴y 1=(-3-6√2)/7,y2=(-3+6√2)/7

∴ vector OA=(x 1, y 1), vector OB=(x2, y2).

Vector OA+ vector OB=(8/7, -3/7)

Vector OP=(8/7λ, -3/7λ)

Line op: y =-3/8x

X 1=-8√ 17 1/57，x2=8√ 17 1/57。

∴y 1=3√ 17 1/57,y2=-3√ 17 1/57

∴8/7λ=8√ 17 1/57

∴λ=7√ 17 1/57