# Dancing On a Parabola

Calculus Level 2

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

×