It is known that the center of ellipse C is the origin of coordinate, the length of minor axis is 2, and a Quasilinear equation is l: x = 2

From the guide line, the focus is on the x-axis
2b=2
b=1
Quasilinear x = A & sup2 / C = 2
a²=2c
a²=b²+c²
So 1 + C & sup2; = 2C
So C = 1
So a & sup2; = 2C = 2
x²/2+y²=1

It is known that the elliptic equation is x ^ 2 / A ^ 2 + y ^ 2 / A ^ 2 = 1, a > b > 0, one of its vertices is m (0,1), and the eccentricity e = √ 6 / 3
(1) The equation for finding ellipse (2) let the distance between O and l of the intersection of line L and ellipse at two points AB be √ 3 / 2, and find the maximum area of △ AOB

E = C / a = root 6 / 3, that is, C ^ 2 / A ^ 2 = 2 / 3 (a ^ 2-B ^ 2) / A ^ 2 = 2 / 3, B ^ 2 / A ^ 2 = 1 / 3, and B = 1 from m (0,1), that is, a ^ 2 = 3, so the elliptic equation is x ^ 2 / 3 + y ^ 2 = 1

RELATED INFORMATIONS

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