Ellipse x ^ 2 / A ^ 2 + y ^ 2 = 1, triangle ABC takes a (0,1) as the right vertex, B, C on the ellipse, the maximum area of triangle is 27 / 8, find the value of A

Ellipse x ^ 2 / A ^ 2 + y ^ 2 = 1, triangle ABC takes a (0,1) as the right vertex, B, C on the ellipse, the maximum area of triangle is 27 / 8, find the value of A

If we know that point a is (0,1), move the coordinate system up to point a, and transform the elliptic equation to: x2 + A2 + (Y-1) 2 = 1 (a > 1); if we transform the Cartesian coordinate system to the polar coordinate system: x = rcosa, y = rsina, we can get (rcosa) 2 + A2 + (rsina-1) 2 = 1 (a > 1); if we simplify it, we can get r = 2sina / (cosa2 / A2 + sina2)