Dancing On a Parabola

Calculus Level 2

Suppose that two people, A and B, walk along the parabola y=x2y=x^2 in such a way that the line segment L L between them is always perpendicular to the line tangent to the parabola at A's position (a,a2)(a,a^2) with a>0 a > 0 . If B's position is (b,b2)(b,b^2), what value of bb minimizes LL?

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