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It is proved that the length of the line segment between two coordinate axes of the tangent at any point on the curve X ^ 2 / 3 + y ^ 2 / 3 = a ^ 2 / 3 (note a > 0 constant, 2 / 3 is power) is fixed
Let a ^ (2 / 3) = a, the original formula can be changed to: y = [A-X ^ (2 / 3)] ^ (3 / 2) = f (x) derivative of X: y = [A-X ^ (2 / 3)] ^ (1 / 2) * [- x ^ (- 1 / 3)] = - [f (x)] ^ (1 / 3) * x ^ (- 1 / 3), so the tangent at (m, n) is: y = - n ^ (1 / 3) * m ^ (- 1 / 3) (x-m) + n let x = 0, y = n ^ (1 / 3) * a let y = 0, x = m ^ (1 / 3) * a lie between the coordinate axes
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