Vector Calculus | Part IA, 2003

Sketch the curve y2=x2+1y^{2}=x^{2}+1. By finding a parametric representation, or otherwise, determine the points on the curve where the radius of curvature is least, and compute its value there.

[Hint: you may use the fact that the radius of curvature of a parametrized curve (x(t),y(t))(x(t), y(t)) is (x˙2+y˙2)3/2/x˙y¨x¨y˙\left(\dot{x}^{2}+\dot{y}^{2}\right)^{3 / 2} /|\dot{x} \ddot{y}-\ddot{x} \dot{y}|.]

Typos? Please submit corrections to this page on GitHub.