Given that point a (0,1) is a point on the ellipse x2 + 4y2 = 4 and point P is a moving point on the ellipse, the maximum length of chord AP is () A. 233B. 2C. 433D. 4

Given that point a (0,1) is a point on the ellipse x2 + 4y2 = 4 and point P is a moving point on the ellipse, the maximum length of chord AP is () A. 233B. 2C. 433D. 4

∵ point P is on the ellipse, | set the coordinates of point P as (2cos θ, sin θ), then | AP | = 4cos2 θ + (sin θ − 1) 2 = − 3 (sin θ + 13) 2 + 163 | when sin θ = - 13, the maximum value of | AP | is 433, so select: C

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