Find the maximum length of the chord AP of a point a (1,0) on the ellipse x ^ 2 + 4Y ^ 2 = 4 Sorry, it's (0, 1) wrong. Sorry

Let P (2cosa, Sina),
|AP|^2=(2cosa)^2+(sina-1)^2
=4(1-sin^2a)+(sin^2a-2sina+1)
=-3sin^2a-2sina+5
This is a quadratic function problem, Sina = - 1 / 3 take the maximum value, is
4 / √ 3 (note the square root)

Through the point B (O, - b), make the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) to find the maximum value of these strings

Through the point B (0, b), make the ellipse (x ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) = 1, (a greater than b greater than 0), and find the maximum length of the chord BP

Let x = acosa, y = bsina
｜BP｜＝√[（acosA）^2+(bsinA-b)^2]=√[（b^2-a^2）sinA^2-2b^2sinA+a^2+b^2]
If you have a specific number, you can substitute it for the maximum value

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