The half focal length of ∴c 1 is c=√5, so a 2-b 2 = 5.
①
Let the coordinate of the intersection of C 1 and y=2x in the first quadrant be (x, 2x), and substitute it into the equation of C 1 to obtain:
x^2=(a^2b^2)/(b^2+4a^2)
②,
According to symmetry, the chord length of the straight line y=2x cut by C65438 +0 =2x√5,
From the topic: 2x√5=2a/3, so x=a/(3√5).
③
② ③ A 2 = 1 1b 2.
④
A 2 = 1 1/2 is obtained from ① ④.
b^2= 1/2