If every tangent line of some curve B(s) which has the unit speed parametrization passes through a fixed point P, then the curve B(s) must be a line.(adsbygoogle = window.adsbygoogle || []).push({});

As a hint, my book says p = B(s) + r(s)B'(s) where r(s) is some function.

so i have that any tangent line L(t) = B(s) + t B'(s) and for some t, L(t) = p = B(s) + r(s)B'(s). i am having trouble continuing with this problem. i cannot think of anything else to do. could someone give me a hint or two on how to proceed? thanks!

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# If every tangent line of a curve passes through a point, it is a line

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